XAT 2021 Geometry & Mensuration Question (Medium)

Question

ABC is a triangle with integer-valued sides AB 1, BC 1, and CA 1. If D is the mid-point of AB, then, which of the following options is the closest to the maximum possible value of the angle ACD in degrees ?

Optima Learn · Accepted Answer

To maximise angle ACD, note that AB 1, so D is the midpoint and AD 0.5. For a fixed triangle ABC, angle ACD is maximised when CD is perpendicular to AB and AC is as small as possible, since sin ACD AD AC. The smallest integer AC 1 is 2. Triangle with sides 1, 2, 2 is valid. Then sin ACD 0.5 2 0.25,

XAT 2021 Geometry & Mensuration — Previous Year Question

XAT 2021

Quantitative

Geometry & Mensuration

Medium

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