perplexus.info :: Geometry : Radius missing

Radius missing (Posted on 2018-03-07)

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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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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