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Radius missing (Posted on 2018-03-07) Difficulty: 3 of 5
This right-angled 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?

See The Solution Submitted by Ady TZIDON    
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Solution Simple solution Comment 2 of 2 |
Let the center of the semicircle be E and the point of tangency F.
ABC~AEF
AE=12-r
So setting up the proportion 13/5=(12-r)/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 2018-03-07 09:09:39
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