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Question 86

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

Solution

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Let us draw the diagram according to the available information.

We can see that triangle BPC and BQC are inscribed inside a semicircle. Hence, we can say that

$$\angle$$ BPC = $$\angle$$ BQC = 90°

Therefore, we can say that BQ  $$\perp$$ AC and CP $$\perp$$ AB.

In triangle ABC,

Area of triangle = (1/2)*Base*Height = (1/2)*AB*CP = (1/2)*AC*BQ

$$\Rightarrow$$ BQ = $$\dfrac{AB*CP}{AC}$$ = $$\dfrac{30*20}{25}$$ = 24 cm.

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