Question 56

Two chords, AB and CD ofcircle meet at a point O, outside the circle. It is given that AB = 7 cm, CD =4 cm, OB = 5 cm. What is the length of OD?

Solution

If two chords, AB and CD of circle meet at a point O, outside the circle then $$OA\times\ OB=OC\times\ OD$$

Given AB=7cm, OB = 5 cm, CD = 4 cm let OD= x

So, OA=12 and OC=4+x

$$12\times\ 5=\left(4+x\right)\times\ x$$

$$x^2+4x-60=0$$

$$x^2+10x-6x+60=0$$

$$x\left(x+10\right)-6\left(x+10\right)=0$$

$$x=6 cm$$

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