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
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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