AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm and AB || CD. If the distance between AB and CD is 3 cm, find the radius of thecircle...... answer it pls...

AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm a

1.	AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm and AB \|\| CD. If the distance between AB and CD is 3 cm, find the radius of thecircle...... answer it pls...
Answer» 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. Draw 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) cmIn right triangles OAP and OCQ, we haveOA2 = 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 cmPutting the values of x in r2 = x2 + 62, we getr2 = 32 + 62 = 45⇒ r = √45 cm = 6.7 cmHence, the radius of the circle is 6.7 cm.