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AP EAMCET202422 May 2024Evening ShiftMathematicsCircleActual

The triangle P Q R is inscribed in the circle x^2+y^2=25 . If Q =(3,4) and R =(-4,3) then QPR =

Options

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

Correct answer

C. 4

Step-by-step solution

The given equation of circle is x^2+y^2=25 Centre is (0,0) and r=5 Now, QR aligned & = (-4-3)^2+(3-4)^2 =5 2 & O Q=O R=5 aligned aligned & ( QOR )= OQ ^2+ OR ^2- QR ^2 2 OQ OR = 25+25-50 2 5 5 =0 & QOR = 2 aligned We know the angle subtended by an arc at the centre is double the angle subtended by same arc at any point on the circle. Now, QOR =2 QPR 2 =2 QRP QPR = 4

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