Beveled corner on a rounded button

Question

I need to create a rounded button with an information badge like this one :

How can I make the beveled corner on the green button around the red information badge ?

I cannot use a normal white border around the red badge (like in the below snippet), because it must be transparent and displays the page background color.

.shape {
  position: relative;
  height: 50px;
  width: 50px;
  border-radius: 50%;
  background: rgb(0, 199, 158);
  margin: 25px;
}
.shape:after {
  position: absolute;
  content: '';
  top: -10px;
  right: -10px;
  height: 25px;
  width: 25px;
  border-radius: 50%;
  border: 3px solid white;
  background: rgb(255, 67, 0);
}
body {
  background: chocolate;
}

<div class='shape'></div>

Answer 1

Using Box Shadow:

One approach would be to use box-shadow on a pseudo-element like in the below snippet. Here, one pseudo-element (.shape:before) is positioned in such a way that it is a bit above the top-right corner of the circle and then its box shadow is used to fill the parent (.container) with required background color. The badge is added via another pseudo-element on the .container element.

This has better browser support than the radial-gradient approach as it works in IE8+. Drawbacks would be that it can only support a solid background color for the main circle as shadows cannot be a gradient or an image. Also, it seems to require two elements (I am trying to reduce it and if successful will add it into answer).

.container {
  position: relative;
  height: 50px;
  width: 50px;
  border-radius: 50%;
  margin: 25px;
}
.shape {
  position: absolute;
  height: 100%;
  width: 100%;
  top: 0px;
  left: 0px;
  border-radius: 50%;
  overflow: hidden;
}
.shape:before {
  position: absolute;
  content: '';
  height: 60%;
  width: 60%;
  top: -20%;
  right: -20%;
  border-radius: 50%;
  box-shadow: 0px 0px 0px 50px rgb(0, 199, 158);
}
.container:after {
  position: absolute;
  content: '2';
  height: 50%;
  width: 50%;
  right: -20%;
  top: -20%;
  background: rgb(255, 67, 0);
  color: white;
  line-height: 25px;
  text-align: center;
  border-radius: 50%;
}

/* just for demo */

*, *:after, *:before {
  transition: all 2s;
}
.container:hover {
  height: 100px;
  width: 100px;
}
.container:hover .shape:before {
  box-shadow: 0px 0px 0px 100px rgb(0, 199, 158);  
}
.container:hover:after {
  line-height: 50px;
}
body {
  background-image: radial-gradient(circle, #3F9CBA 0%, #153346 100%);
  min-height: 100vh;
}

<div class='container'>
  <div class='shape'></div>
</div>

---

Using Radial Gradient:

Another option would be to use radial-gradient for background-image like in the below snippet and position the background such that it produces a beveled corner on the top right. Once its done, adding the badge circle and positioning it should be fairly straight-forward.

This has poorer browser support compared to the box-shadow approach as it works only in IE10+. If responsiveness is required then using gradients would be a better option as they can take percentage values unlike box shadows.

.shape {
  position: relative;
  height: 50px;
  width: 50px;
  border-radius: 50%;
  background-image: radial-gradient(60% 60% at 92.5% 7.5%, transparent 49.5%, rgb(0,199,158) 50.5%);
  margin: 25px;
}
.shape:after {
  position: absolute;
  content: '2';
  height: 50%;
  width: 50%;
  right: -20%;
  top: -20%;
  background: rgb(255,67,0);
  color: white;
  line-height: 25px;
  text-align: center;
  border-radius: 50%;
}

/* just for demo */

*, *:after {
  transition: all 1s;
}
.shape:hover {
  height: 100px;
  width: 100px;
}
.shape:hover:after {
  line-height: 50px;
}
body {
  background-image: radial-gradient(circle, #3F9CBA 0%, #153346 100%);
}

<div class='shape'></div>

---

Using SVG:

Another possibility would be to make use of SVG to create the beveled circle like in the below snippet.

.shape {
  position: relative;
  height: 50px;
  width: 50px;
  border-radius: 50%;
  margin: 25px;
}
svg {
  position: absolute;
  height: 100%;
  width: 100%;
}
svg path {
  fill: rgb(0, 199, 158);
}
.shape:after {
  position: absolute;
  content: '2';
  height: 50%;
  width: 50%;
  right: -25%;
  top: -5%;
  background: rgb(255, 67, 0);
  color: white;
  line-height: 25px;
  text-align: center;
  border-radius: 50%;
}

/* just for demo */

*, *:after {
  transition: all 2s;
}
.shape:hover {
  height: 100px;
  width: 100px;
}
.shape:hover:after {
  line-height: 50px;
}
body {
  background-image: radial-gradient(circle, #3F9CBA 0%, #153346 100%);
}

<div class='shape'>
  <svg viewBox='0 0 60 60'>
    <path d='M55,30 A25,25 0 0,1 5,30 A25,25 0 0,1 42.5,8.34 A16,16 0 0,0 55,30' />
  </svg>
</div>

Note: I've used pseudo-element for the badge just for illustration but since you'd need to add dynamic content into it, I'd recommend replacing that with a child element.