Q: 2     Two chords AB and CD of lengths \small 5\hspace {1mm}cm and \small 11\hspace {1mm}cm 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 \small 6\hspace {1mm}cm, find the radius of the circle.

Answers (1)

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

To find Radius (OA).

Construction: Draw OM \perp CD \, \, and \, \, \, ON\perp AB

Proof : 

          

Proof: CD is a chord of circle  and  OM \perp CD

    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 \triangle OCM , using pythagoras,

                 OC ^2=CM^2+OM^2.............................1

and

In \triangle OAN , using pythagoras,

                 OA ^2=AN^2+ON^2.............................2

From 1 and 2,

      CM ^2+OM^2=AN^2+ON^2            (OC=OA =radii)

      5.5 ^2+x^2=2.5^2+(6-x)^2

\Rightarrow 30.25+x^2=6.25+36+x^2-12x

\Rightarrow 30.25-42.25=-12x

\Rightarrow -12=-12x

\Rightarrow x=1

From 2, we get 

OC^2=5.5^2+1^2=30.25+1=31.25

\Rightarrow OC=\frac{5}{2}\sqrt{5} cm

OA = OC 

Thus, the radius of the circle is \frac{5}{2}\sqrt{5} cm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

               

Most Viewed Questions

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/-
Buy Now
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/-
Buy Now
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/-
Buy Now
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/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

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

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions