Question

In the given figure, BOC is a diameter of a circle with centre O. If
AB and CD are two chords such that AB || CD and AB = 10 cm, then CD =
(a) 5 cm
(b) 12.5 cm
(c) 15 cm
(d) 10 cm
​

Answer 1

Construct OL⊥AB and OM⊥CD

Consider △OLB and △OMC

We know that ∠OLB and ∠OMC are perpendicular bisector

∠OLB=∠OMC=90

o

We know that AB∥CD and BC is a transversal

From the figure we know that ∠OBL and ∠OCD are alternate interior angles

∠OBL=∠OCD

So we get OB=OC which is the radii

By AAS congruence criterion

△OLB≅△OMC

OL=CM (c.p.c.t.)

We know that the chords equidistant from the centre are equal so we get

AB=CD

So, AB = 10cm

CD = 10cm

Answer 2

Answer:

10 cm is the length of CD.

Step-by-step explanation: