This rightangled triangle ABC has sides of lengths:
AC=12cm, BC=5cm and AB=13cm.
1. The diameter CD of the semicircle lies on the 12cm side.
2. The AB side is a tangent to the circle.
What is the radius R of the semi circle?
Let the center of the semicircle be E and the point of tangency F.
ABC~AEF
AE=12r
So setting up the proportion 13/5=(12r)/r
Gives r=10/3
[This can easily generalize to a right triangle with legs, a and b and hypotenuse c with the diameter on the side b. r=(ab)/(a+c)]

Posted by Jer
on 20180307 09:09:39 