Question

In the given figure, O is the centre of the
circle, AB and CD are two chords of
the circle. OM is perpendicular to AB and
ON is perpendicular to CD. AB = 24 cm,
OM = 5 cm, ON = 12 cm. Find the :
(i) radius of the circle.
(ii) length of chord CD.




Answer as fast as possible...looking for step-by-step explanations...​

Answer 1

Answer:

Step-by-step explanation:

Given : AB = 24 cm, OM = 5 cm, ON =12 cm

OM⊥AB

M is the midpoint of AB

AM=12cm

(i) Radius of circle OA=  

OM  

2

+AM  

2

 

​  

 

OA=  

5  

2

+12  

2

 

​  

=  

25+144

​  

=  

169

​  

=13

(ii) Again OC  

2

=ON  

2

+CN  

2

        ∵OC=OA

13  

2

=12  

2

+CN  

2

 

CN=  

13  

2

−12  

2

 

​  

=  

169−144

​  

=  

25

​  

 

CN=5cm

As ON⊥CD, N is the mis-point of CD

CD=2CN=2×5=10 cm