Question

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at
a point Q so that OQ = 12 cm. Length PQ is:
(A) 12 cm (B) 13 cm (C) 8.5 cm (D)root of 119 cm.​

Answer 1

Here Is Your Ans ⤵

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The Tangent At Any Point OF a Circle Is Perpendicular To The Radius Through The Point OF Contact

Ans :-

➡√119

Given :-

➡OP = 5 Cm

➡OQ = 12 Cm

➡Angle P = 90°

To Find :-

➡PQ = ?

Solution :-

➡Angle P = 90°

By Phythagores Theorem ,

$\implies { OQ }^{2} = {PQ }^{2} + {OP }^{2} \\ \\ \implies PQ = \sqrt{ {OQ }^{2} - {OP }^{2} }$

Hence , Length Of PQ Is $\fbox{ \fbox{ \sqrt{119} }}$ Cm

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Answer 2

Answer:

the answer is as folow

Step-by-step explanation:

√119

Given :-

➡OP = 5 Cm

➡OQ = 12 Cm

➡Angle P = 90°

To Find :-

➡PQ = ?

Solution :-

➡Angle P = 90°

By Phythagores Theorem ,

\begin{lgathered}\implies { OQ }^{2} = {PQ }^{2} + {OP }^{2} \\ \\ \implies PQ = \sqrt{ {OQ }^{2} - {OP }^{2} }\end{lgathered}

⟹OQ

2

=PQ

2

+OP

2

⟹PQ=

OQ

2

−OP

2

Hence , Length Of PQ Is \fbox{ \fbox{ \sqrt{119} }}

119

Cm