Answer to Question #240282 in Geometry for 0.0

Question

QC is a median of triangle PQR. The incircle of triangle PQR intersects this median at points A and B, and at that A lies between Q and B, and QA : AB : BC=1:2:1. Find the ratio of the largest side of triangle PQR to its smallest side.

Answer 1

If the incircle intersect median of a triangle it has to be a right angle triangle and because its ratio is 1:2:1 the triangle is to be isosceles right angle triangle

therefore the smaller side be 2A

so $2a^2+2a^2=b^2$ (here b is hypotenuse )

so $\frac{b}{a}= 2 \sqrt 2$