In the figure, AB is diameter and PQ is tangent. If PQ=5 cm and PA=1 cm , then the radius of circle is

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In the figure, $A B$ is diameter and $P Q$ is tangent. If $P Q = 5 c m$ and $P A = 1 c m$ , then the radius of circle is

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13 c m

11 c m

12 c m

7 c m

answer is B.

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Detailed Solution

In $Δ P Q O, ∠ P Q O = 90 °$

$P O^{2} = P Q^{2} + O Q^{2}$

${(P A + A O)}^{2} = P Q^{2} + O Q^{2}$

${(1 + r)}^{2} = 5^{2} + r^{2}$

$1 + r^{2} + 2 r = 25 + r^{2}$

$1 + 2 r = 25$

$2 r = 24$

$r = 12 c m$ .

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