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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» <html><body><p>Let <a href="https://interviewquestions.tuteehub.com/tag/ab-360636" style="font-weight:bold;" target="_blank" title="Click to know more about AB">AB</a> 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, <a href="https://interviewquestions.tuteehub.com/tag/q-609558" style="font-weight:bold;" target="_blank" title="Click to know more about Q">Q</a> and P are collinear. Clearly, PQ = <a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a> 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 <a href="https://interviewquestions.tuteehub.com/tag/equating-7679226" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATING">EQUATING</a> 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.</p></body></html>


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