31. 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.
Answers
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
Radius of circle = 8 cm
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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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