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Question

In a triangle PQR, let PQR=30 and the sides PQ and QR have lengths 103 and 10, respectively. Then, which of the following statement(s) is (are) TRUE?

A
QPR=45
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B
The area of the triangle PQR is 253 and QRP=120
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C
The radius of the incircle of the triangle PQR is 10315
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D
The area of the circumcircle of the triangle PQR is 100 π
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Solution

The correct option is D The area of the circumcircle of the triangle PQR is 100 π

By cosine law,
cos30=100+300(PR)22×10×103
PR=10
PR=QR, then QPR=PQR
QPR=30 and QRP=120
area(PQR),=12×103×10sin30=253

Radius of incircle is given by
r=S=25312(10+10+103)=10315

Radius of the circumcircle is
R=PR2sin30=10
Therefore, area of the circumcircle =π(10)2=100 π

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