2017 · Q61
Segment QR of length r is a tangent at Q to a circle of radius r with centre at P. What is the area of the part of the triangle PQR, which is outside the circular region ?
Elementary MathematicsCircles
- A(π r²)/16
- Br²/2 - (π r²)/8
- Cr²/2 - (π r²)/16
- Dr²/4 - (π r²)/8
Explanation
∠PQR = 90° (radius ⊥ tangent), and PQ = QR = r, so the triangle's area is r²/2 and ∠QPR = 45°. The sector of the circle inside the triangle has area (45/360)πr² = πr²/8. The part outside = r²/2−πr²/8. Hence option (B).