Question 72

AB and CD are two chords of a circle which intersect at a point O inside the circle. It is given that, AB = 10 cm, CO = 1.5 cm and DO = 12.5 cm. Whatis the ratio between the larger and smaller among AO and BO ?

Solution

By the property of circle two chords intersect then,

$$AO\times OB = CO\times DO$$

AB = 10 , Let AO be the larger = x and BO = 10 - x

$$x\times (10 -x) = 1.5\times 12.5$$

$$x^{2}-10x = 1.5\times12.5$$

$$x^{2}-10x+18.75=0$$

$$x^{2}-2.5x-7.5x+18.75=0$$

x = 7.5 and 2.5

AO is larger so AO = 7.5 and BO = 2.5

Required ratio = 7.5 : 2.5 = 3 : 1

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