Question

. AB is a tangent to a circle with centre P and B is the point of contact. PA Intersects
the circle at C. If AB = 15 cm and AC = 9 cm, find the radius of the circle​

Answer 1

Given : AB is a tangent to a circle with centre P and B is the point of contact.  

PA Intersects the circle at C.

AB = 15 cm and AC = 9 cm,

To find :  the radius of the circle​

Solution:

AP² = AB²  + PB²

PB = r  cm = Radius of circle

AP = AC + CP

CP = Radius of circle

=> AP = 9 + r  cm

AB = 15 cm

=> (9 + r)² = 15² + r²

=> 81 + r² + 18r = 225 + r²

=>18r = 144

=> r = 8  cm

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Answer 2

Given :- AB is a tangent to a circle with centre P and B is the point of contact. PA intersects the circle at C if AB = 15cm, AC = 9cm .

To Find :-

• Radius of the circle ?

Solution :-

Let us assume that, radius of the circle is r cm.

we know that,

• A tangent to a circle is perpendicular to the radius through the point of contact .

so,

→ ∠ PBA = 90°

now, in right angled ∆PBA , we have,

→ PB² + AB² = PA²

→ r² + 15² = (9 + r)²

→ r² + 225 = 81 + r² + 18r

→ 18r = 225 - 81

→ 18r = 144

→ r = 8 cm. (Ans.)

Hence, Radius of the circle is 8 cm.

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