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

Answer 1

Refer to the below diagram
Observe that triangle BPC and BQC are inscribed inside a semicircle. Hence,
∠BPC = ∠BQC = 90°
Therefore, we can say that BQ ⊥ AC and CP ⊥ AB.
Also, In triangle ABC,
Area of triangle = (1/2)×Base×Height = (1/2)×AB×CP = (1/2)×AC×BQ
⇒ BQ = AB×CP / AC = 30×20/25 = 24 cm.