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ARIEN3228
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Angle PAQ is common in both triangles.

Mo2men
nick1816
∠ APC = ∠AQB = 90

Triangle APC is similar to Triangle AQB.

AC/AB = PC/BQ

25/30 = 20/BQ

BQ = 24


Hi nick1816

How did you establish the similarity? I see only one angle (90) that can help here.
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We need to find length of a diameter and we know that a diameter is the longest cord in a circle. Also we know length of cord CP = 20. So, can we also say that length of diameter CB will be more then 20. Since we just have one option in answer choice which is more then 20, answer is 24.
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ARIEN3228
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

A)8
B)6√2
C)24
D)12
E) 6

Discussed here: on-a-triangle-abc-a-circle-with-diameter-bc-is-drawn-intersecting-ab-314238.html?fl=similar

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