Circular Measure Long Questions (Question 4)


Question 4:

In the diagram above, AXB is an arc of a circle centre O and radius 10 cm with ÐAOB = 0.82 radian. AYB is an arc of a circle centre P and radius 5 cm with ÐAPB = θ. Calculate:
(a) the length of the chord AB,
(b) the value of θ in radians,
(c) the difference in length between the arcs AYB and AXB.

Solution:
(a)
1 2 AB=sin0.41×10 1 2 AB=3.99 The length of chord AB=3.99×2=7.98 cm.
(b)
Let  1 2 θ=α, θ=2α sinα= 3.99 5 α=0.924 rad θ=0.924×2=1.848 radian.
(c)
                        Using s =
                        Arcs AXB = 10 × 0.41 = 4.1 cm
                        Arcs AYB = 5 × 1.848 = 9.24 cm

                        Difference in length between the arcs AYB and AXB
                        = 9.24 – 4.1
                        = 5.14 cm