In a #DeltaAOB# inscribed in a circle, its legs #OA=10cm.# and #OB=24cm.# and #AB# is the largest chord of the circle. What is the radius of the circle?

1 Answer
Feb 1, 2018

Radius is #13cm.#

Explanation:

As #AB# is the largest chord, it is diameter and #AB# divides the circle in two semicircles.

Ends of a semicircle subtends right angle at any point on the circumference and hence at #O# too.

Therefore #DeltaAOB# is right angled at #O# and #OA# and #OB# are its two legs.

Now using Pythagorus Theorem

#AB^2=10^2+24^2=100+576=676#

Hence #AB=sqrt676=26#

i,e. diameter of circle is #26cm.# and its radius is #13cm.#