Question

In the given figure, AB is the diameter of the circle. If C is a point on the circle such that angle ADC = 60 degree , then angle BAC is ______.

Answer 1

Answer:

30

As angle ADB is 90 (angle inscribed in semicircle)

Answer 2

The angle of BAC is 30.

Given,

ADC = 60

AB is diameter

Since,

ADB is angle subtended by diameter so, ADB = 90.

Also, ACD = ABD as they are angles subtended by same segment. ----(1).

Name the point of intersection as O.

AOC = BOD ----(2).

By AA similarity criteria,

In triangle AOC and triangle DOB,

ACD = ABD ---(1)

AOC = BOD ---(2)

So, by AA criteria, angle OCA = angle ODB.

Since, ADB = ADC + ODB.

90 = 60 + ODB.

ODB = 30.

Since, ODB = 30 and due to AA similarity criteria BAC = 30.