Question

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Question is in the attachment above.


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Answer 1

Required Answer:-

Refer to the attachment...

AP is the tangent to the circle from exterior point P and AC is one of the radius. As AP is touching the circle at A, A is the point of tangency.

Then,

According to tangent, radius theoram: Tangent is perpendicular to radius at point of tangency i.e. < PAC = 90° here.

Let AC = x, then BC will also be x because AC and BC both are the radii of the circle. Now, let's apply Pythagoras theoram.

$\because{ \boxed{\sf{\purple{ {p}^{2} + {b}^{2} = {h}^{2} }}}}$

Putting the corresponding sides,

➛ AC² + AP² = CP²

➛ x² + 24² = (x + 16)²

➛ x² + 576 = x² + 32x + 256

➛ 32x + 256 = 576

➛ 32x = 320

➛ x = 10

And we consider radius to be x.

Then, radius of the circle will be equal to 10 cm (Ans).

Answer 2

Answer:

Given :-

PA = 24 cm

PB = 16 cm

To Find :-

Radius

Solution :-

By using the Pythagoras theorem

$\bf \red{P^2 = H^2 + B^2}$

$\bf \pink{AC^2 + AP^2 = CP^2}$

Let the radius be x cm

x² + 24² = (x + 16)²

x² + 576 = x² + 32x + 256

Cancelling x²

576 = 32x + 256

576 - 256 = 32x

320 = 32x

320/32 = x

10 = x