Question

In a circle of radius 13cm, AB is a chord and OP is perpendicular to AB . If OP = 5cm, find the length of AB​

Answer 1

Answer:

24

Step-by-step explanation:

first you draw a circle, draw chord AB(not passing through the centre) and from the centre draw OP to AB such that OP⊥AB. Now join OA and OB. They become the two radii of the circle. now,

in triangle APO

OA^2- OP^2= AP^2                       (PYTHAGORUS THEOREM)

=>13^2-5^2=AP^2

=>169-25=AP^2

=>144=AP^2

=>AP=12

WE KNOW THAT A PERPENDICULAR FROM THE CENTRE OF A CIRCLE TO A CHORD BISECTS IT

=>AP=PB=12

=>AP+PB=12+12

=>AB=24

Answer 2

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