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Question 6

From Math Analysis HL Paper 2 (May 2025, TZ2)

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  1. [Maximum mark: 6]

The following diagram shows a circle with centre O and radius r cmr \text{ cm}. Points A and B lie on the circle and AÔB = θ\theta radians. Sector OAB is divided into two regions, a shaded segment P and a triangle Q.

A circle with center O and radius r. Points A and B are on the circle. Angle AOB is theta radians. The sector OAB is divided into a shaded segment P and a triangle Q.
A circle with center O and radius r. Points A and B are on the circle. Angle AOB is theta radians. The sector OAB is divided into a shaded segment P and a triangle Q.

The area of the shaded segment P is 12.8 cm212.8 \text{ cm}^2.

The areas of P and Q are in the ratio 3:5.

Find the value of rr.