Target Mathematics

1.21: Sector arc length and angle

4PM1/2/June/2024 — Question 3 · 6 marks

1.21 diagram 1
Figure 1 shows the sector AOBAOB of a circle with centre OO and radius 3r3r cm
A circle with radius rr cm touches OAOA and OBOB and the arc ABAB
Angle AOBAOB is θ\theta radians, where 0<θ<π20 < \theta < \frac{\pi}{2}
(a) Find the exact value of θ\theta
(2)
The area of the region shown shaded in Figure 1 is 8π8\picm2\mathrm{cm}^{2}
(b) Find the value of rr
(4)