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  ∠AOB = 0.82 radian. AYB is an arc of a circle centre P and radius 5 cm with  ∠APB = 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( Change the calculator to Rad mode ) 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 × 0.82 = 8.2 cm
Arcs AYB = 5 × 1.848 = 9.24 cm

Difference in length between the arcs AYB and AXB
= 9.24 – 8.2
= 1.04 cm

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