Question

Two chords of lengths 10cm and 24cm are drawn parallel o each other in a circle. If they are on the same side of the centre and the distance between them is 17cm, find the radius of the circle.

Answer 1

CP = PO = 12cm 

Let OA = OC = r (say) 

Also, let OQ = x,  ∴  OP = 17 - x 

In right Δ OPC, 

By Pythagoras theorem, 

OC² = OP² + PC² 

r² = (17- x)² + 122 ----( 1 ) 

Similarly, In Δ OQA, 

OA² = AQ² + QO² 

r² = 5² + x² ----(2}

From (1) and { 2} 

( 17 - x)² + 12² = 52 + x² 

289 - 34 x + 144 - 25 = 0 

34x = 408 

x = 12

From {2} 

r² = 5² + 12² 

25+ 144= 169 

r = 13 

The radius of the circle is 13cm .