C is a point on the minor arc AB of the circle with the centre O given angleACB =X - Maths - Constructions

Question

C is a point on the minor arc AB of the circle with the centre O
given angleACB =X degree and angleAOB=y degree, express y in terms
of x calculate x, if ACBO is a parallelogram

Manbar Singh · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_59a172ca4ff5b%20png"
style="width: 222px; height: 240px;">
We have,∠AOB = y; ∠ACB = xNow, reflex∠AOB = 360°-∠AOB = 360°-yWe know that angle subtended by an arc at the centre is double the angle subtended by same arc at any point on the circle
So, reflex∠AOB = 2∠ACB⇒360°-y = 2x⇒y = 360° - 2x    
1 Since, AOBC is a parallelogram, then∠AOB = ∠ACB   Opposite angles of parallelogram are equal⇒y = xNow, from 1, we getx = 360° - 2x⇒3x = 360°⇒x = 120°

C is a point on the minor arc AB of the circle with the centre O .given angleACB =X degree and angleAOB=y degree, express y in terms of x.calculate x, if ACBO is a parallelogram