P is a point outside a circle and is 13 cm away from its centre. A secant drawn from the point P intersects the circle at points A and B in such a way that PA =9 cm and AB= 7 cm. The radius of the circle is [SSC (CGL) 2012] |
A) 5.5 cm
B) 5 cm
C) 4 cm
D) 4.5 cm
Correct Answer: B
Solution :
Let the radius of circle be r. |
From figure, |
\[PA\times PB=PQ\times PR\] |
\[\Rightarrow \] \[9\times (9+7)=(13-r)(13+r)\] |
\[\Rightarrow \] \[169-{{r}^{2}}=144\]\[\Rightarrow \]\[{{r}^{2}}=25\] |
\[\Rightarrow \] \[r=5\,\,cm\] |
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