chore(examples): add Radix UI example (vercel#41169)

fixes vercel#40072 

## Documentation / Examples

- [ ] Make sure the linting passes by running `pnpm lint`
- [x] The "examples guidelines" are followed from [our contributing doc](https://github.com/vercel/next.js/blob/canary/contributing/examples/adding-examples.md)


Co-authored-by: Balázs Orbán <18369201+balazsorban44@users.noreply.github.com>

examples/radix-ui/.gitignore

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+# Dependencies
+/node_modules
+/.pnp
+.pnp.js
+
+# Testing
+/coverage
+
+# Next.js
+/.next/
+/out/
+
+# Production
+/build
+
+# Misc
+.DS_Store
+*.pem
+
+# Debug
+npm-debug.log*
+yarn-debug.log*
+yarn-error.log*
+.pnpm-debug.log*
+
+# Local env files
+.env*.local
+
+# Vercel
+.vercel
+
+# typescript
+*.tsbuildinfo
+next-env.d.ts

examples/radix-ui/README.md

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+# Radix UI Example
+
+This example showcases a few basic Radix UI components
+
+## Deploy your own
+
+Deploy the example using [Vercel](https://vercel.com?utm_source=github&utm_medium=readme&utm_campaign=next-example):
+
+[![Deploy with Vercel](https://vercel.com/button)](https://vercel.com/new/git/external?repository-url=https://github.com/vercel/next.js/tree/canary/examples/radix-ui&project-name=radix-ui&repository-name=radix-ui)
+
+## How to use
+
+Execute [`create-next-app`](https://github.com/vercel/next.js/tree/canary/packages/create-next-app) with [npm](https://docs.npmjs.com/cli/init), [Yarn](https://yarnpkg.com/lang/en/docs/cli/create/), or [pnpm](https://pnpm.io) to bootstrap the example:
+
+```bash
+npx create-next-app --example radix-ui radix-ui-app
+```
+
+```bash
+yarn create next-app --example radix-ui radix-ui-app
+```
+
+```bash
+pnpm create next-app --example radix-ui radix-ui-app
+```
+
+Deploy it to the cloud with [Vercel](https://vercel.com/new?utm_source=github&utm_medium=readme&utm_campaign=next-example) ([Documentation](https://nextjs.org/docs/deployment)).

examples/radix-ui/package.json

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+{
+  "private": true,
+  "scripts": {
+    "dev": "next dev",
+    "build": "next build",
+    "start": "next start"
+  },
+  "dependencies": {
+    "@radix-ui/react-dropdown-menu": "1.0.0",
+    "@radix-ui/react-icons": "1.1.1",
+    "next": "latest",
+    "react": "latest",
+    "react-dom": "latest"
+  },
+  "devDependencies": {
+    "@types/node": "18.8.0",
+    "@types/react": "18.0.21",
+    "autoprefixer": "10.4.12",
+    "postcss": "8.4.17",
+    "tailwindcss": "3.1.8",
+    "typescript": "4.8.4"
+  }
+}

examples/radix-ui/pages/_app.tsx

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+import '../styles/globals.css'
+
+export default function MyApp({ Component, pageProps }) {
+  return <Component {...pageProps} />
+}

examples/radix-ui/pages/index.tsx

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+import { useState } from 'react'
+import {
+  HamburgerMenuIcon,
+  DotFilledIcon,
+  CheckIcon,
+  ChevronRightIcon,
+} from '@radix-ui/react-icons'
+import * as DropdownMenu from '@radix-ui/react-dropdown-menu'
+
+function RightSlot({ children }) {
+  return (
+    <div className="ml-auto pl-4 text-gray-500 group-hover:text-gray-200">
+      {children}
+    </div>
+  )
+}
+
+function DropdownMenuItem({ children, ...props }) {
+  return (
+    <DropdownMenu.Item
+      {...props}
+      className={
+        'group bg-white hover:bg-gray-700 hover:text-gray-200 text-xs rounded flex items-center h-6 px-1 pl-6 relative select-none' +
+        (props.disabled ? ' text-gray-500' : '')
+      }
+    >
+      {children}
+    </DropdownMenu.Item>
+  )
+}
+
+function DropdownMenuCheckboxItem({ children, ...props }) {
+  return (
+    <DropdownMenu.CheckboxItem
+      {...props}
+      className="group bg-white hover:bg-gray-700 hover:text-gray-200 text-xs rounded flex items-center h-6 px-1 pl-6 relative select-none"
+    >
+      {children}
+    </DropdownMenu.CheckboxItem>
+  )
+}
+
+function DropdownMenuItemIndicator({ children, ...props }) {
+  return (
+    <DropdownMenu.ItemIndicator
+      {...props}
+      className="absolute left-0 w-6 inline-flex items-center justify-center"
+    >
+      {children}
+    </DropdownMenu.ItemIndicator>
+  )
+}
+
+function Separator() {
+  return <DropdownMenu.Separator className="h-[1px] bg-gray-300 m-1" />
+}
+
+function DropdownMenuRadioItem({
+  children,
+  ...props
+}: {
+  children: React.ReactNode
+  value: string
+}) {
+  return (
+    <DropdownMenu.RadioItem
+      {...props}
+      className="bg-white hover:bg-gray-700 hover:text-gray-200 text-xs rounded flex items-center h-6 px-1 pl-6 relative select-none"
+    >
+      {children}
+    </DropdownMenu.RadioItem>
+  )
+}
+
+export default function Home() {
+  const [bookmarksChecked, setBookmarksChecked] = useState(true)
+  const [urlsChecked, setUrlsChecked] = useState(false)
+  const [person, setPerson] = useState('pedro')
+  return (
+    <div className="h-screen w-full flex flex-col space-y-4 items-center justify-center bg-gradient-to-r from-cyan-500 to-blue-500">
+      <h1 className="text-6xl text-white font-semibold">
+        Radix UI + Tailwind CSS
+      </h1>
+      <h1 className="text-4xl text-white font-semibold">Click me!</h1>
+
+      <DropdownMenu.Root>
+        <DropdownMenu.Trigger
+          asChild
+          className="bg-white text-xs rounded-3xl flex items-center h-8 px-2 relative select-none"
+        >
+          <button
+            aria-label="Customise options"
+            className="h-8 w-8 inline-flex items-center justify-center shadow-lg"
+          >
+            <HamburgerMenuIcon />
+          </button>
+        </DropdownMenu.Trigger>
+
+        <DropdownMenu.Content
+          sideOffset={5}
+          className="bg-white rounded p-1 shadow-lg"
+        >
+          <DropdownMenuItem>
+            New Tab <RightSlot>⌘+T</RightSlot>
+          </DropdownMenuItem>
+          <DropdownMenuItem>
+            New Window <RightSlot>⌘+N</RightSlot>
+          </DropdownMenuItem>
+          <DropdownMenuItem disabled>
+            New Private Window <RightSlot>⇧+⌘+N</RightSlot>
+          </DropdownMenuItem>
+          <DropdownMenu.Sub>
+            <DropdownMenu.SubTrigger className="group bg-white hover:bg-gray-700 hover:text-gray-200 hover:border-0 text-xs rounded flex items-center h-6 px-1 pl-6 relative select-none">
+              More Tools
+              <RightSlot>
+                <ChevronRightIcon />
+              </RightSlot>
+            </DropdownMenu.SubTrigger>
+            <DropdownMenu.SubContent
+              sideOffset={2}
+              alignOffset={-5}
+              className="bg-white rounded p-1 shadow-lg"
+            >
+              <DropdownMenuItem>
+                Save Page As… <RightSlot>⌘+S</RightSlot>
+              </DropdownMenuItem>
+              <DropdownMenuItem>Create Shortcut…</DropdownMenuItem>
+              <DropdownMenuItem>Name Window…</DropdownMenuItem>
+              <Separator />
+              <DropdownMenuItem>Developer Tools</DropdownMenuItem>
+            </DropdownMenu.SubContent>
+          </DropdownMenu.Sub>
+          <Separator />
+          <DropdownMenuCheckboxItem
+            checked={bookmarksChecked}
+            onCheckedChange={setBookmarksChecked}
+          >
+            <DropdownMenuItemIndicator>
+              <CheckIcon />
+            </DropdownMenuItemIndicator>
+            Show Bookmarks <RightSlot>⌘+B</RightSlot>
+          </DropdownMenuCheckboxItem>
+          <DropdownMenuCheckboxItem
+            checked={urlsChecked}
+            onCheckedChange={setUrlsChecked}
+          >
+            <DropdownMenuItemIndicator>
+              <CheckIcon />
+            </DropdownMenuItemIndicator>
+            Show Full URLs
+          </DropdownMenuCheckboxItem>
+          <Separator />
+          <DropdownMenu.Label className="pl-6 leading-6 text-xs text-gray-700">
+            Contributors
+          </DropdownMenu.Label>
+
+          <DropdownMenu.RadioGroup value={person} onValueChange={setPerson}>
+            <DropdownMenuRadioItem value="pedro">
+              <DropdownMenuItemIndicator>
+                <DotFilledIcon />
+              </DropdownMenuItemIndicator>
+              Pedro Sanchez
+            </DropdownMenuRadioItem>
+            <DropdownMenuRadioItem value="pablo">
+              <DropdownMenuItemIndicator>
+                <DotFilledIcon />
+              </DropdownMenuItemIndicator>
+              Pablo Sanchez
+            </DropdownMenuRadioItem>
+          </DropdownMenu.RadioGroup>
+        </DropdownMenu.Content>
+      </DropdownMenu.Root>
+    </div>
+  )
+}

examples/radix-ui/postcss.config.js

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+module.exports = {
+  plugins: {
+    tailwindcss: {},
+    autoprefixer: {},
+  },
+}

examples/radix-ui/styles/globals.css

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+@tailwind base;
+@tailwind components;
+@tailwind utilities;

examples/radix-ui/tailwind.config.js

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+/** @type {import('tailwindcss').Config} */
+module.exports = {
+  content: ['./pages/**/*.{js,ts,jsx,tsx}'],
+  theme: {
+    extend: {},
+  },
+  plugins: [],
+}

examples/radix-ui/tsconfig.json

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+{
+  "compilerOptions": {
+    "target": "es5",
+    "lib": ["dom", "dom.iterable", "esnext"],
+    "allowJs": true,
+    "skipLibCheck": true,
+    "strict": false,
+    "forceConsistentCasingInFileNames": true,
+    "noEmit": true,
+    "incremental": true,
+    "esModuleInterop": true,
+    "module": "esnext",
+    "moduleResolution": "node",
+    "resolveJsonModule": true,
+    "isolatedModules": true,
+    "jsx": "preserve"
+  },
+  "include": ["next-env.d.ts", "**/*.ts", "**/*.tsx"],
+  "exclude": ["node_modules"]
+}