Answer:
r = 12
Step-by-step 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.
