Right angled problem

Geometry Level 3

A right triangle is divided into two smaller triangles when an altitude is drawn towards the hypotenuse. If the distance between the in centers of the two smaller triangles is 14, find the inradius of the original triangle. Give your answer in decimals upto 3 digits


The answer is 9.89.

Varun Srinivas by varun srinivas , 21, India

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2 solutions

Ahmad Saad
Nov 20, 2016

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Ajit Athle
Jun 3, 2015

Consider a right triangle with sides AB=30, BC=40 & CA=50. Drop a perpendicular BD, from B to AC.. Triangle BAD will have an in-radius of 6 while triangle BCD will have an in-radius of 8. The in-radius of tr. ABC will be =(30+40-50)/2 =10 and not 9.89 as suggested by the problem-setter. In any case, what is your method of calculation? --------- A²

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