# Q: 2     Two chords AB and CD of lengths and respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is , find the radius of the circle.

Given : AB = 5 cm, CD = 11 cm and AB || CD.

Construction: Draw

Proof :

Proof: CD is a chord of circle  and

Thus, CM = MD = 5.5 cm    (perpendicular from centre bisects chord)

and      AN = NB  = 2.5 cm

Let OM be x.

So, ON = 6 - x              (MN = 6 cm )

In  OCM , using pythagoras,

.............................1

and

In  OAN , using pythagoras,

.............................2

From 1 and 2,

From 2, we get

OA = OC

Thus, the radius of the circle is

## Related Chapters

### Preparation Products

##### Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
##### Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
##### NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
##### NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-