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In the diagram, point P is a point of tangency. Find the radius r of circle O.​

In the diagram, point P is a point of tangency. Find the radius r of circle O.​-example-1

2 Answers

4 votes

Answer:

r=12

Explanation:

User Yantao Xie
by
8.3k points
0 votes

Answer:

r = 12

Explanation:

From the figure attached,

QP is a tangent to the circle O at the point P.

Therefore, by the property of tangency,

OP ⊥ QP

By applying Pythagoras theorem In right triangle QPO,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

(OQ)² = (OP)² + (PQ)²

(25 + r)² = (35)² + r²

625 + r² + 50r = 1225 + r²

50r = 1225 - 625

50r = 600

r = 12

Therefore, r = 12 units is the answer.

User Umer
by
8.2k points

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