Question 79

In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of chord PQ is

Solution

$$\frac{AX}{BX} =\frac{3}{2}$$

$$AX = \frac{3}{5} \times 10 = 6cm $$

$$BX = \frac{2}{5} \times 10 = 4cm $$

$$AX \times XB = PX^2$$

$$PX^2 = \sqrt{6 \times 4} = 2\sqrt{6}$$

PQ = 2PX = $$ 4\sqrt{6}$$

So, the answer would be option c)4$$\surd{6}$$ cm

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