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In a circle of centre O, PR = 3a + 5 and RQ = 5a – 5, OR = 15 units, ∠ORP = 90°. Find the radius of the circle.

image.png

A20

B25

C30

D15

Answer:

B. 25

Read Explanation:

We know that perpendicular from the centre of the circle to the chord,  bisects the chord.

⇒ OR bisects the chord PQ.

⇒ PR = RQ

⇒ 3a + 5 = 5a – 5

⇒ a = 5

⇒ PR = RQ = 3 × 5 + 5 = 5 × 5 – 5 = 20

Using Pythagoras theorem,

⇒ OQ2 = OR2 + RQ2

⇒ OQ2 = 152 + 202

⇒ OQ = 25

Radius of circle is 25 units.


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