Question

(c)
In the given diagram 'O' is the centre of the circle and AB is parallel to CD.
AB = 24 cm and distance between the chords AB and CD is 17 cm. If the radius
of the circle is 13 cm, find the length of the chord CD.​

Answer 1

Answer:

Do you now get it... It is made easy in this photo

Answer 2

Given:-

AB|| CD

AB = 24 cm

Distance between the chords AB and CD

= 17 cm.

The radius of the circle

= 13 cm.

To find = The length of chord CD.

Solution-

- Let M and N be the mid points of the chord AB and CD respectively.

So, MN = 17 cm ...(given)

MO = NO = 8.5

Where O will be the mid point of MN.

-*Join AD and BC*

Now, in ΔAOM and ΔCON

angle AMO = angle CNO......(90°)

MO = NO ...(proved above)

AO = CO ...(radius of circle)

- So, By RHS theoram

ΔAMO is congurent to ΔCON

AM = CN......(1)

- Similarly, in ΔBOM and ΔDON

angle BMO = angle DNO...(90°)

MO = NO...(proved above)

BO=DO ...(radius of circle)

-So, by RHS theoram ΔBOM is congurent to ΔDON

BM = DN......(2)

- By adding (1) and (2)

AM + BM = CN + DN

*So ,AB = CD = 24cm*