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An acute triangle PQR is inscribed in th...

An acute triangle PQR is inscribed in the circle `x^2+y^2= 25`. If Q and R have coordinates (3, 4) and (-4, 3) respectively, then find `/_QPR`.

A

`pi//2`

B

`pi//3`

C

`pi//4`

D

`pi//6`

Text Solution

Verified by Experts

The correct Answer is:
C
Let O is the point at centre and P is the point at circumference. Therefore, angle QOR is double the angle QPR. So, it is sufficient to find the angle QOR.

Now, Slope of ` OQ, m_(1)=4//3`,
Slope of `OR, m_(2)=-3//4`
Here, `m_(1)m_(2)=-1`
therefore, `angle QOR = pi//2`
which implies that `ange QPR = pi//4`
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