Ab And Cd Are Two Parallel Chords Of Circle Such That Ab 10 Cm And Cd 24 Cm

AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the … between them is 17 cm, find the radius…

Answers:

Let O be the centre of the given circle and let it’s radius be r cm. Draw OP ⊥ AB and OQ ⊥ CD. Since,  AB ∥ CD. Therefore, points  P , O and Q are collinear. So,  PQ = 17 cm.

Let OP = x cm, Then, OQ = (17 – x) cm

Join OA  and OC.  Then, OA = OC = r.

Since, the perpendicular from the centre to a chord of the circle bisects the chord.

∴  AP = PB = 5 cm and CQ = QD = 12 cm

In right triangles OAP and OCQ, we have

OA² = OP² + AP² and OC² = OQ² + CQ²

⇒  r² = x² + 5²       …….(i)

and    r² = (17 – x)² + 12²     …..(ii)

⇒  x² + 5² = ( 17 – x)² + 12²    [On equating the values of r² ]

⇒  x² + 25 = 289 – 34x + x² + 144

⇒   34x = 408   ⇒  x = 12 cm.

Putting  x = 12 cm in (i), we get

r² = 12² + 5² = 169 ⇒ r = 13 cm

hence, the radius of the circle is 13 cm.