Question

Two chords AB and CD of lengths 6cm and 12cm are drawn parallel inside the circle. If the distance between the chords of the circle is 3cm, find the radius of the circle.

Answer 1

AP = PB = 3cm 

CQ = QD = 6cm (Perpendicular from centre to a chord bisects the chord) 

OA = OC = r (say) 

Let OP = x,  ∴  OQ = 3 - x 

In right Δ OQC,

By Pythagoras theorem, 

OC² = OQ² + CQ² 

r² = (3-x)² + 6² ----(1) 

Similarly, In Δ OPA, 

OA² = AP² + PO²  

r² = 3² + x² ----(2} 

From (1) and {2} 

(3-x)² + 6² = 3²+ x² 

-6x + 36 = 0

x = 6

from {2}

r² = 3² + 6² = 9 + 36 = 45 

r = `3 sqrt 5`

Thus , radius of the circle is `3 sqrt 5` cm