CAT 2018 [SLOT 2] Quant Question with Solution 06

Question:
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

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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