Question

ab and cd are two chords of a circle such that ab=6 cm cd=12 cm

Answer 1

Step-by-step explanation:

Let AB and CD be two parallel chords of a circle with centre O such that AB = 6 cm CD = 12 cm. Let the radius of the circle be r cm. Drwa OP ⊥ AB and OQ ⊥ CD. Since,  AB ∥ CD and OP ⊥ AB, OQ ⊥ CD. Therefore points  O, Q  and P are collinear. Clearly, PQ = 3 cm.

Let OQ = x cm. Then, OP = (x + 3) cm

In right triangles OAP and OCQ, we have

OA2 = OP2 + AP2 and OC2 = OQ2 + CQ2

⇒ r2 = (x + 3)2 + 32   and  r2 = x2 + 62

[∵  AP = ½ AB = 3 cm and CQ = ½ CD = 6  cm

⇒  (x + 3)2 + 32 = x2 + 62      (on equating the value of r2)

⇒  x2 + 6x + 9 + 9  = x2 + 36

⇒  6x = 18  ⇒  x = 3 cm

Putting the values of x in r2 = x2 + 62, we get

r2 = 32 + 62 = 45

⇒  r = √45 cm = 6.7 cm

Hence, the radius of the circle is 6.7 cm.