Question

In the circle shown below, The length of chord AB is 24 and the length of OC is 5. What is the radius of the circle with center O

Answer 1

13

Explanation:

AB is bisected by perpendicular OC so AB is divided into intwo two equal halves.

if AB = 24

AC =
`(1)/(2) *AB`

=
`(1)/(2) *24`

=12

no join OA and name its length as x

OA = X

OC = 5

AC = 12

when u join O and A it forms a triangle . SO to find OA lets find pythagoras theorem

OC^2 + AC^2 = OA^2

5^2 + 12^2 = OA^2

25 + 144 = OA^2

169 = OA^2

`√(169)` = OA

13 = OA

radius is the line joining the centre and any point on the circumference.So here since O is the centre and A is the points on the circumference and they are joined so the line can be named as radius of a circle.

Therefore radius of a circle is 13

Answer 2

radius = 13

Explanation:

OC is a perpendicular bisector of AB , then AC = 12

OA is the radius of the circle

Using Pythagoras' identity in right triangle OAC

OA² = OC² + AC²

OA² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )

OA =
`√(169)` = 13

The radius = 13 units