Question

Two chords AB and CD of lengths 5 cm and 11 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 6 cm, find the radius of the circle.
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Answer 1

Question ⤵

Two chords AB and CD of lengths 5 cm and 11 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 6 cm, find the radius of the circle.

Answer ⬇

Refer to the attachement. Kindly see.

Hope it helps.

Thanks..

Answer 2

Answer:

Given :

two chords AB and CD of length 5 cm and 11 cm respectively of a circle are parallel to each other and are on the same side of the centre.

distance between AB and CD is 3 cm

To Find  :

radius of the circle.

Solution:

Distance from center to mid point of Chord CD =  x cm

Distance from center to mid point of Chord AB =  x+3 cm

R = Radius of circle

=> R² = x² +  (11/2)²

   R² = (x + 3)² + (5/2)²

Equating R²

=>  (x + 3)² + (5/2)² = x² +  (11/2)²

=> x² + 6x + 9 + 25/4 = x² + 121/4

=>  6x  + 61/4 = 121/4

=> 6x = 60/4

=> x = 10/4

=> x = 5/2

R² = x² +  (11/2)²

=>  R² = (5/2)² +  (11/2)²

=> R² =   146/4

=> R = √146 / 2

=> R = 6.04 cm

Radius of circle = 6.04 cm

hope this helps you