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CAT 2018 Slot 2 — QA Question 20

Similarity of TrianglesEasy

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

Answer & solution

Answer: 24

Solution

Since points P and Q lie on the circumference of the circle drawn with BC as diameter, angles BPC and BQC are right angled triangles.

Now, area of triangle ABC = 12×AB×PC = 12×AC×BQ

Therefore, BQ = AB×PCAC = 30×2025 = 24

Hence, 24.

CAT 2018 Slot 2 QA Q20: On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. — Solution | TheCATExam