Question

A, B and C are points on a circle.

EF is a tangent to the circle at C.
D is a point on AC.
Angle CBD:Angle ABD = 3:1.
Find angle ADB.
Give a geometrical reason for each step of your working.

Answer 1

44/3 degrees

Explanation:

Angle CBD = 180 - (64 + 72) = 44

Angle ADB = 44/3 (Since of the ratio)

Answer 2

In the figure, angle ADB is equal to 98 degrees

How to find angle ADB

Angle FCA = angle CBA = 72 (angle intercepts equal arc)

angle BCD = 180 - 64 - 72

angle BCD = 44egrees

angle BAC = 180 - angle BCD - angle CBA

angle BAC = 180 - 44 - 72

angle BAC = 64degrees

OR

angle BAC = angle BCE = 64 (angle intercepts equal arc)

angle ABD = 1/4 angle CBA

angle ABD = 1/4 * 72

angle ABD = 18 degrees

angle ADB = 180 - angle ABD - angle BAC

angle ADB = 180 - 18 - 64

angle ADB = 98 degrees