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Question

# Find the area of the right triangle whose one side passes through the center of the circle having a radius of 5 units and base of the triangle lies on a chord of length 8 cm.

A
8 unit2
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B
16 unit2
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Solution

## The correct option is B 16 unit2The given figure is as follows: P is the center of the circle. PZ=5 units (radius) The given triangle is right triangle. ∴∠XQY=90o Hence, PQ bisects the chord ZY at the midpoint Q. ⇒ZQ=QY=82=4 units For △PZQ, PZ2=ZQ2+PQ2 ⇒PQ2=PZ2−ZQ2=52−42=32 ⇒PQ=3 units Now, XP is also the radius of the circle. ∴XQ=XP+PQ=5+3=8 units Area of △XYQ =12×XQ×QY =12×8×4 unit2 =16 unit2

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