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Question

In the given figure, $$AB$$ and $$AC$$ are tangents to the circle at $$B$$ and $$C$$, respectively, and $$O$$ is the centre of the circle, then $$x$$ equals


A
3cm
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B
4cm
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C
5cm
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D
6cm
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Solution

The correct option is C $$5\;cm$$
From the figure, PAO forms a right angled triangle.
Now, $$  QA = AR = \frac {7}{2}  cm = 3.5 cm $$
And $$ PA = PQ + AQ = 9 + 3.5 = 12.5  cm $$
Now, $$ {OP}^{2} = {PA}^{2} + {OA}^{2} $$
$$ => {13}^{2} = {12.5}^{2} + {OA}^{2} $$
$$ {OA}^{2} = 12.75 $$
Now, triangle OAQ will also be a right angled triangle.
$$ => {OQ}^{2} = {QA}^{2} + {OA}^{2} = {3.5}^{2} + 12.75 = 25 $$
$$ => OQ = Radius = 5  cm $$
364966_328754_ans_bc863b9882ce4d6d96697951db9a0dee.png

Mathematics

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