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Manipal MET2012MathematicsProperties of Triangles

The P Q R is inscribed in the circle x^2+y^2=25 . If Q and R have coordinates (3,4) and (-4,3) , respectively. Then, Q P R is equal to

Options

  1. A2
  2. B3
  3. C4
  4. D6

Correct answer

C. 4

Step-by-step solution

Let O is the point on centre and P is the point on circumference. Therefore, angle QOR is double the angle QPR. So, it is sufficient to find the angle Q O R . Now, slope of O Q, m₁= 4-0 3-0 = 4 3 Slope of O R, m₂= 3-0 -4-0 =- 3 4 Again, m₁ m₂=-1 Therefore, Q O R=90^ Which implies that Q P R= 90^ 2 =45^ .

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