Aryan geometry challenge 3

Geometry Level 5

let triangle ABC be a right angled at B. let D be a point on AC such that the inradii of the triangle ABD and CBD are equal to 3. Also the inradius of ABC=5.FIND BD.


The answer is 7.5.

Aryan Goyat by aryan goyat , 22, India

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2 solutions

Vinod Kumar
May 7, 2019

(1/3)-(1/5)=(1/BD) gives BD Answer=7.5

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Rajdeep Brahma
Apr 3, 2017

Use some trig manipulation to show that 1 R \frac{1}{R} = 1 r \frac{1}{r} + 1 B D \frac{1}{BD} .(Refer to INMO 2016).

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I don't think this triangle is possible. How can BD be less than the diameter of the larger incircle?

Bob Kadylo - 3 years, 5 months ago

1 pending report

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