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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 unit2
The 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=PZ2ZQ2=5242=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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