A geometry problem by Sankalp Sahay

Geometry Level 1

In the figure given below, PQ and PR are tangents to the circle from an external point P. O is the center of the circle. If QPR = 50°, find QSR.

75 85 65 45

Sankalp Sahay by Sankalp Sahay , 32, India

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1 solution

  1. QP and SQ are Perpendicular (the tangent is perpendicular to the radius)
  2. Construct radius OR
  3. OR is perpendicular to RP
  4. Angle ROQ is 130 (Sum of interior angles of quadrilateral)
  5. Angle SOR is 50 (Supplemental angle to ROQ)
  6. Segments OS and OR are congruent (they are both radii)
  7. Triangle OSR is Isosceles
  8. Angle OSR = ORS
  9. 50 + 2x = 180 (Triangle sum theorem)
  10. Angle QSR is 65 degrees
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