Question

AB and CD are two parallel chords of a circle such that AB=10 cm. If chords are on opposite sides of the centre of the circle and the distance between them is 17 cm, find the radius of the circle.

Answer 1

Answer:

r=13cm

step by step explaination:

Let radius of the circle be r

given,MN=17cm

let ON=x

then, OM=17-x

Angle AOM,

OA^2=OM^2+AM^2

=> r^2={17-x}^2+5^2

289+x^2-34x+25

r^2=314+x^2-34x__(1)

OC^2=ON^2 +CN^2

=> r^2=x^2+12^2=x^2+144__(2)

from eqs.(1) and (2),we get

314+x^2-34x=x^2+144

=>34x=170

=>x=5

eq (2) r^2=25+144=169

r=13cm

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