If $A B$ is tangent to the circle at $A$ and $O B = 13$ cm, find the radius $O A$ .

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Solution

The correct option is B $5$ cm
$O A ⊥ A B$
(Tangent is perpendicular to the radius)
${O B}^{2} = {O A}^{2} + {A B}^{2}$
$13^{2} = {O A}^{2} + 12^{2}$
${O A}^{2} = 169 - 144 = 25$
$O A = 5$ cm

So, option A is correct.

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If AB is tangent to the circle at A and OB=13 cm, find the radius OA.

The correct option is B 5 cmOA⊥AB(Tangent is perpendicular to the radius)OB2=OA2+AB2132=OA2+122OA2=169−144=25OA=5cmSo, option A is correct.

If $A B$ is tangent to the circle at $A$ and $O B = 13$ cm, find the radius $O A$ .

The correct option is B $5$ cm
$O A ⊥ A B$
(Tangent is perpendicular to the radius)
${O B}^{2} = {O A}^{2} + {A B}^{2}$
$13^{2} = {O A}^{2} + 12^{2}$
${O A}^{2} = 169 - 144 = 25$
$O A = 5$ cm

So, option A is correct.