Question

6. In the figure, seg CD is a diameter.
m(arc BXC) = 2x® and
m(arc BYD) = 3xº
Find (1) m(arc BCD) (2) m(arc BYD) (3) m(arc CDB)
Ans. ​

Answer 1

We have O  as the centre of circle

join OA

we know that line segment joining the centre to the midpoint of the chord is perpendicular to the chord 

Now, OE⊥AB

we have, Let,OC=xcm=OA(radiiofthecircle)andOE=OC−EC=(x−3)cmInΔOEAOA2=OE2+AE2⇒x2=(x−3)2+42⇒x=625⇒x=4.16cm