Question 70
Two chords AB and CD of a circle intersectat a point O insidethe circle. It is given that AO = 1 cm, AB = 13 cm, CD= 8 cm. What is the ratio between the larger and smaller section among CO and OD ?
Solution
Two chords AB and CD of a circle intersect at a point O inside the circle then,
$$AO\times\ OB\ =\ CO\times\ OD$$
Let CO be x cm and its larger one. So, OD = (8 - x) cm
$$1\times\ 12=x\left(8-x\right)$$
$$12=8x-x^2$$
$$x^2-8x+12=0$$
$$x^2-6x-2x+12=0$$
$$x\left(x-6\right)-2\left(x-6\right)$$
$$x=6,\ 2$$
So, CO = 6 and OD = 2
CO:OD = 6:2 = 3:1
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