O IS THE CENTRE OF THE CIRCLE IF ANGLE AOB= 80 degree THEN FIND THE MEASURE OF ANGLE ADB - Maths - Circles

Question

O IS THE CENTRE OF THE CIRCLE IF ANGLE AOB= 80 degree THEN FIND THE
MEASURE OF ANGLE ADB AND ANGLE ACB PLEASE PROVIDE THE DIAGRAM

Manbar Singh · Accepted Answer

Dear student,
You have not provided the information about the points C and D, so
I am taking point C in the major segment of circle and D in the
minor segment of the circle
Here is the solution

We know that angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle
Consider the minor arc AB, that subtends ∠AOB at the centre and ∠ACB on the circle
Now, ∠AOB = 2∠ACB⇒∠ACB = ∠AOB2 = 80°2 = 40°Since ADBC, is a cyclic quadrilateral, then∠ADB + ∠ACB = 180°   Opposite angles of cyclic quadrilateral are supplementary⇒∠ADB + 40° = 180°⇒∠ADB = 140°

O IS THE CENTRE OF THE CIRCLE. IF ANGLE AOB= 80 degree THEN FIND THE MEASURE OF ANGLE ADB AND ANGLE ACB.PLEASE PROVIDE THE DIAGRAM.