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Standard Values of Trigonometric Ratios

In the given ...

Question

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

3 c m

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4 c m

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5 c m

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6 c m

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Solution

The correct option is C $5 c m$
From the figure, PAO forms a right angled triangle.
Now, $Q A = A R = \frac{7}{2} c m = 3.5 c m$
And $P A = P Q + A Q = 9 + 3.5 = 12.5 c m$
Now, ${O P}^{2} = {P A}^{2} + {O A}^{2}$
$=> 13^{2} = {12.5}^{2} + {O A}^{2}$
${O A}^{2} = 12.75$
Now, triangle OAQ will also be a right angled triangle.
$=> {O Q}^{2} = {Q A}^{2} + {O A}^{2} = {3.5}^{2} + 12.75 = 25$
$=> O Q = R a d i u s = 5 c m$

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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

The correct option is C 5cmFrom the figure, PAO forms a right angled triangle. Now, QA=AR=72cm=3.5cmAnd PA=PQ+AQ=9+3.5=12.5cm Now, OP2=PA2+OA2=>132=12.52+OA2 OA2=12.75 Now, triangle OAQ will also be a right angled triangle. =>OQ2=QA2+OA2=3.52+12.75=25=>OQ=Radius=5cm

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