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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