AB is a chord of a circle with centre O If P is any point on minor arc AB, - Maths - Circles

Question

AB is a chord of a circle with centre O If P is any point on minor
arc AB, prove that angle AOB + 2 angle APB = 360

Samarpita Choudhury · Accepted Answer

AOB = 360 - Reflex AOB ( Complete angle ) (i)
​2APB = Reflex AOB ( Since, angle at the centre is double the
angle at the circumference) (ii)
From (i) and (ii), we get,
AOB = 360 - 2 APB
​=> AOB + 2APB = 360
HENCE PROVED

AB is a chord of a circle with centre O. If P is any point on minor arc AB, prove that angle AOB + 2 angle APB = 360.