Question

in figure A,B and,C are three points on a circle with center o such that angle BOC =30 AND ANGLE AOB =60 . IF D IS A POINT ON THE CIRCLE OTHER THAN THE ARC ABC ,FIND ANGLE ADC ​

Answer 1

Answer:

45° or 30°

Depending upon ABC point position

Step-by-step explanation:

in figure A,B and,C are three points on a circle with center o such that angle BOC =30 AND ANGLE AOB =60 . IF D IS A POINT ON THE CIRCLE OTHER THAN THE ARC ABC ,FIND ANGLE ADC ​

As figure is missing there could be few cases for position of ABC point

ABC  ,  ACB   , BAC

case 1 as ABC

∠AOC  = Arc Angle

∠AOC = ∠AOB + ∠BOC

=> ∠AOC = 60° + 30

=>∠AOC = 90°

∠ADC = (1/2) ∠AOC

=> ∠ADC = (1/2) * 90°

=> ∠ADC = 45°

Case 2 ACB

∠AOB is the arc Angle

∠ADC = (1/2) ∠AOB

=>  ∠ADC = (1/2) * 60°

=> ∠ADC = 30°

Case 3 BAC is not possible as

∠AOB > ∠ BOC

so A   can not lie between BC points

Answer 2

Answer:

45° or 30°

Depending upon ABC point position

Step-by-step explanation:

in figure A,B and,C are three points on a circle with center o such that angle BOC =30 AND ANGLE AOB =60 . IF D IS A POINT ON THE CIRCLE OTHER THAN THE ARC ABC ,FIND ANGLE ADC ​

As figure is missing there could be few cases for position of ABC point

ABC  ,  ACB   , BAC

case 1 as ABC

∠AOC  = Arc Angle

∠AOC = ∠AOB + ∠BOC

=> ∠AOC = 60° + 30

=>∠AOC = 90°

∠ADC = (1/2) ∠AOC

=> ∠ADC = (1/2) * 90°

=> ∠ADC = 45°

Case 2 ACB

∠AOB is the arc Angle

∠ADC = (1/2) ∠AOB

=>  ∠ADC = (1/2) * 60°

=> ∠ADC = 30°

Case 3 BAC is not possible as

∠AOB > ∠ BOC

so A   can not lie between BC points

Step-by-step explanation: