Question 70

In a circle, AB is a the diameter and CD is a chord. AB and CD produced meet at a point P, outside the circle. If PD = 15.3 cm, CD = 11.9 cm and AP = 30.6 cm,then the radius of the circle is is:

Solution

From the property,

PA $$\times PB = PC \times PD$$

30.6 $$\times PB = (PD + CD) \times 15.3$$

30.6 $$\times PB = (15.3 + 11.9) \times 15.3$$

30.6 $$\times PB = 27,2 \times 15.3$$

PB = 416.16/30.6 = 13.6 cm

Diameter (AB) = PA - PB = 30.6 - 13.6 = 17 cm

Radius = AB/2 = 17/2 = 8.5 cm

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