Circles

Geometry Level 3

In the fig. given below, O is the center of the circle. If PA = 12cm, PC = 15cm and CD = 7cm. Find length of AB.


The answer is 2.

Gurjot Sodhi by Gurjot Sodhi , 23, Canada

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2 solutions

Gurjot Sodhi
Oct 14, 2014

Let PB = x cm Then PA * PB = PC * PD

12 * x = 15 * (15-7)

x = 10 cm

PB = 10 cm

AB = 12 – 10 = 2 cm

3 Helpful 0 Interesting 0 Brilliant 0 Confused

nice but i applied another approach

Drishtdyumn Shrivastava - 5 years, 3 months ago

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Plz elaborate, I qould love to see your approach.

Ashish Menon - 5 years, 1 month ago

Relevant wiki: Power of a Point

By Power of a point , we have

P B ( P A ) = P D ( P C ) PB(PA)=PD(PC)

( 12 − A B ) ( 12 ) = 8 ( 15 ) (12-AB)(12)=8(15)

144 − 12 A B = 120 144-12AB=120

144 − 120 = 12 B 144-120=12B

24 = 12 B 24=12B

B = 2 \boxed{B=2}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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