CircleHard

Question

The triangle PQR is inscribed in the circle x2 + y2 = 25 . If Q and R have coordinates (3, 4) and (-4,3) respectively, then ∠QPR is equal to

Options

A.π /2
B.π / 3
C.π / 4
D.π / 6

Solution

       
LetO is the point at centre and P is the point at circumference. Therefore, angleQOR is double the angleQPR. So it is sufficient to find the angleQOR.
Now, slope of OQ m1 = 4 / 3, slope of OR, m2 = - 3 / 4
Here,       m1m2 = - 1
Therefore,     ∠QOR = π / 2
which implies that ∠QPR = π / 4

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