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Question is in the attachment above.
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Answers
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.
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:
Given :-
PA = 24 cm
PB = 16 cm
To Find :-
Radius
Solution :-
By using the Pythagoras theorem
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