Question

in figure chord AB is equal to radius find angle ACB and angle ADB. ​

Answer 1

Answer:

AB is the cord in the circle.

2Angle ACB= AOB.

AOB/2= ACB.

angle subtended by an Arc of the circle is double to the remaining part of the circle.

ACB+ADB=180°

opposite angle of cyclic quadrilateral are supplementary.

Answer 2

Answer:

Angle ACB = 30°

Angle ADB = 150°

Step-by-step explanation:

AO = BO = AB

Therefore, ∆AOB is an equilateral triangle.

All angles of an equilateral triangle is 60°

Therefore, Angle AOB = 60° ....... (1)

Angle ACB & Angle AOB are inscribed angles of the circle since they have common endpoints A & B.

Using Inscribed Angle Theorem,

Angle ACB = 1/2 of Angle AOB ...... Theorem

Angle ACB = 1/2 of 60° ....... From (1)

Angle ACB = 30° ...... (2)

ACBD forms a quadrilateral in the circle.

Therefore,

Angle ACB + Angle ADB = 180° ..... Sum of the opposite angles of a quadrilateral is 180°

Therefore,

30° + Angle ADB = 180° ..... From (2)

Angle ADB = 180° - 30°

Angle ADB = 150°