Long Questions (Question 8)

Posted on May 16, 2020 by Myhometuition

Question 8:

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)

\begin{array}{l} \frac{1}{2} A B = \sin 0.41 \times 10 \to (Change the calculator to Rad mode) \\ \frac{1}{2} A B = 3.99 \\ ∴ The length of chord A B = 3.99 \times 2 = 7.98 c m . \end{array}

(b)

\begin{array}{l} Let \frac{1}{2} θ = α, θ = 2 α \\ \sin α = \frac{3.99}{5} \\ α = 0.924 rad \\ ∴ θ = 0.924 \times 2 = 1.848 radian . \end{array}

(c)

Using s = rθ

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