CAT 2018 Quant Questions

On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is

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Correct Answer: 24

Refer to the below diagram

Observe that triangle BPC and BQC are inscribed inside a semicircle. Hence,

\(\angle \) BPC = \(\angle \) BQC = 90°

Therefore, we can say that BQ \( \bot \) AC and CP \( \bot \) AB.

Also, In triangle ABC,

Area of triangle = (1/2)×Base×Height = (1/2) ×AB×CP = (1/2) ×AC×BQ

\( \Rightarrow \) BQ = \(\frac{{AB×CP}}{{AC}}\) = \(\frac{{30×20}}{{25}}\) = 24 cm.

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