Question 126

P is a point outside a circle with centre O, and it is 14 cm away from the centre. A secant PAB drawn from P intersects the circle at the points A and B such that PA = 10 cm and PB = 16 cm. The diameter of the Circle is:

Solution

From the above question, we draw the diagram is given below

Let $$x = Radius of circle OP = 14 cm, OD = x = OE $$

Now, according to Secant theirem,

$$ 10 \times 16 = (14-x) (14+x) $$

$$\Rightarrow x^2= (14)^2-160 $$

$$\Rightarrow x^2 =36 $$

$$\Rightarrow x = 6 cm $$

so, Diameter = $$2x = 2 \times 6 = 12 $$ cm Ans

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