XAT 2024 Geometry & Mensuration Question (Medium)

Question

Consider a right-angled triangle ABC, right angled at B. Two circles, each of radius r, are drawn inside the triangle in such a way that one of them touches AB and BC, while the other one touches AC and BC. The two circles also touch each other see the image . If AB 18 cm and BC 24 cm, then find the

Optima Learn · Accepted Answer

Place the triangle on the coordinate plane with B at the origin B 0,0 , C 24,0 , A 0,18 . Then AB is the y-axis and BC is the x-axis. The hypotenuse AC has equation 3x 4y - 72 0 since the triangle is 18-24-30 . Let the circle touching AB and BC have centre O_1 r,r and radius r distance r from both a

XAT 2024 Geometry & Mensuration — Previous Year Question

XAT 2024

Quantitative

Geometry & Mensuration

Medium

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