### Ab And Cd Are Two Chords Of Circle Such That Ab 6 Cm Cd 12 Cm And Ab В€Ґ Cd

**AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm and AB ∥ CD. If the … AB and CD is 3 cm, find the radius of…**

###### Answers:

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

OA^{2} = OP^{2 }+ AP^{2} and OC^{2} = OQ^{2} + CQ^{2}

⇒ r^{2} = (x + 3)^{2} + 3^{2 } and r^{2} = x^{2} + 6^{2}

^{}

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

⇒ (x + 3)^{2} + 3^{2} = x^{2} + 6^{2} (on equating the value of r^{2})

⇒ x^{2} + 6x + 9 + 9 = x^{2} + 36

⇒ 6x = 18 ⇒ x = 3 cm

Putting the values of x in r^{2} = x^{2} + 6^{2}, we get

r^{2} = 3^{2} + 6^{2} = 45

⇒ r = √45 cm = 6.7 cm

Hence, the radius of the circle is 6.7 cm.