Question

A circle with centre O in which a diameter AB bisects the chord PQ at the point R. If PR = RQ = 8cm and RB = 4cm , find the radius of the circle.

Answer 1

given... AB is the diameter and PQ is the chord of the circle with centre O and AB bisects PQ at R also   PR = RQ = 8 cm and RB = 4 cm
we know that the line from the centre of the circle which bisects the chord is perpendicular to the chord
⇒ AB ⊥ PQ
Let the radius of the circle be r
⇒ OP = OB = r
⇒ OR + RB = r
⇒ OR = r – RB = r-4
Now in right ∆ ORP
OR²+PR²=OP²
⇒ (r – 4)²+8²=R²
⇒r²+4²-2*4*r+64=r²
⇒16-8r+64=0
⇒8r=80
⇒r=80/8
⇒r=10
∴RADIUS 10 

Answer 2

given... AB is the diameter and PQ is the chord of the circle with centre O and AB bisects PQ at R also   PR = RQ = 8 cm and RB = 4 cm

we know that the line from the centre of the circle which bisects the chord is perpendicular to the chord

⇒ AB ⊥ PQ

Let the radius of the circle be r

⇒ OP = OB = r

⇒ OR + RB = r

⇒ OR = r – RB = r-4

Now in right ∆ ORP

OR²+PR²=OP²

⇒ (r – 4)²+8²=R²

⇒r²+4²-2*4*r+64=r²

⇒16-8r+64=0

⇒8r=80

⇒r=80/8

⇒r=10

∴RADIUS 10