In the diagram O and O’ are the centres of the circles radii 15cm and 8cm…

In the diagram O and O’ are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OO’|.

Correct Answer: Option B

Explanation

 In (Delta) POQ, 

(12^2 = 15^2 + 15^2 – 2(15)(15) cos < POQ)

(144 = 450 – 450cos < POQ)

(450 cos < POQ = 450 – 144 = 306)

(cos <POQ = frac{306}{450} = 0.68)

(< POQ = 47.2°)

In (Delta) PO’Q, 

(12^2 = 8^2 + 8^2 – 2(8)(8) cos <PO’Q)

(144 – 128 = -128 cos < PO’Q)

(cos < PO’Q = – 0.125)

(< PO’Q = 97.2°)

In (Delta) POQ,

(cos 23.6 = frac{x}{15})

(x = 15 times cos 23.6)

= 13.75 cm

In (Delta) PO’Q, 

(cos 48.6 = frac{y}{8})

(y = 8 times cos 48.6)

= 5.29 cm

(therefore) OO’ = x + y = 13.75 + 5.29

= 19.04 cm