The length of a tangent drawn from a point A is 12cm which is 13cm away from the centre of the circle. Find the diameter of the circle.

Question

Satt Academy · Accepted Answer

প্রশ্নে বলা হচ্ছে যে, বৃত্তের বহিঃস্থ একটি বিন্দু A হতে বৃত্তের উপর অঙ্কিত স্পর্শকের দূরত্ব 12cm এবং কেন্দ্র থেকে A বিন্দুর দূরত্ব 13cm হলে বৃত্তটির ব্যাস কত?

We depict the following figure according to question.

Here, OB is perpendicular on base AB.

So, clearly AO is hypotenuse

Now, applying Pythagorean law, we get

$O A^{2} = O B^{2} + A B^{2}$

$\Rightarrow O B^{2} = O A^{2} - A B^{2} = 13^{2} - 12^{2} = 169 - 144 = 25 ∴ O B = \sqrt{25} = \sqrt{5^{2}} = 5 ∴ O B = 5 c m$

Here, OB is radius of the circle and we know that the diameter of a circle is twice of the radius.

$∴ D i a m e t e r = 5 \times 2 = 10 c m . (a n s .)$

OA2 = OB2 + AB2 ⇒ OB2 = OA2-AB2 = 132-122 = 169-144 = 25

The length of a tangent drawn from a point A is 12cm which is 13cm away from the centre of the circle. Find the diameter of the circle.
(Geometry (Circle))

Question:
The length of a tangent drawn from a point A is 12cm which is 13cm away from the centre of the circle. Find the diameter of the circle.
(Geometry (Circle))

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The length of a tangent drawn from a point A is 12cm which is 13cm away from the centre of the circle. Find the diameter of the circle. (Geometry (Circle))

Question: The length of a tangent drawn from a point A is 12cm which is 13cm away from the centre of the circle. Find the diameter of the circle. (Geometry (Circle))

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The length of a tangent drawn from a point A is 12cm which is 13cm away from the centre of the circle. Find the diameter of the circle.
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Question:
The length of a tangent drawn from a point A is 12cm which is 13cm away from the centre of the circle. Find the diameter of the circle.
(Geometry (Circle))