Question

In a circle with centre O and radius 13cm, AB is a chord. If OM is perpendicular to AB and OM=5cm, what is the length of AB​

Answer 1

Given,

A circle with centre O and radius 13cm and AB is a chord and OM is perpendicular to AB and OM is 5cm

To find,

length of chord AB.

solution,

length of chord AB = AM + MB

Therefore let first find AM and MB

In right angled triangle AOM

OM, perpendicular is 5cm

OA, Radius of circle is 13cm

AM, base of triangle OR 1/2 length of chord is ??

so , pyhthagoras theorem can be use here

H2 = B2 + P2

13 * 13 = AM2 + 5*5

169 = AM 2 + 25

169 - 25 = AM2

144 = AM2

√144= AM

AM = 12

similarly, In right angled triangle OMB

MB = 12cm

hence, the length of chord = AM + MB

= 12 + 12

= 24cm