HTML5 / CSS3 Circle with Partial Border

Yes, it is possible – see this:

demo

.circle {
  position: relative;
  margin: 7em auto;
  width: 16em;
  height: 16em;
  border-radius: 50%;
  background: lightblue;
}

.arc {
  overflow: hidden;
  position: absolute;
  /* make sure top & left values are - the width of the border */
  /* the bottom right corner is the centre of the parent circle */
  top: -1em;
  right: 50%;
  bottom: 50%;
  left: -1em;
  /* the transform origin is the bottom right corner */
  transform-origin: 100% 100%;
  /* rotate by any angle */
  /* the skew angle is 90deg - the angle you want for the arc */
  transform: rotate(45deg) skewX(30deg);
}

.arc:before {
  box-sizing: border-box;
  display: block;
  border: solid 1em navy;
  width: 200%;
  height: 200%;
  border-radius: 50%;
  transform: skewX(-30deg);
  content: '';
}
<div class="circle">
  <div class="arc"></div>
</div>

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