In the given figure, AB is the diameter of the circle and ZCBA = 50°,

1.	In the given figure, AB is the diameter of the circle and ZCBA = 50°, then the measure of Z CDB is equal to
Answer» Answer: ∠CAB = 40°. Step-by-step EXPLANATION: AB is the DIAMETER of the circle with center at O. C is a POINT on the circle. Given that ∠CBA = 50°. Now, in ΔOCB, OC = OB [∵ Radius of the same circle] ∴ ∠OCB = ∠OBC = ∠ABC = ∠CBA = 50°. ∠AOC = ∠OCB + ∠OBC [∵ ∠AOC is exterior angle of ΔOCB] ∴ ∠AOC = 50° + 50° = 100° And in ΔOCA, OC = OA [∵ Radius of the same circle] ∴ ∠OCA = ∠OAC = $\frac{1}{2}$ (180° - ∠AOC) = $\frac{1}{2}$ (180° - 100°) = 40° ∴ ∠CAB = ∠CAO = ∠OAC = 40°.

In the given figure, AB is the diameter of the circle and ZCBA = 50°, then the measure of Z CDB is equal to

Answer»

Answer:

∠CAB = 40°.

Step-by-step EXPLANATION:

AB is the DIAMETER of the circle with center at O.

C is a POINT on the circle.

Given that ∠CBA = 50°.

Now, in ΔOCB, OC = OB [∵ Radius of the same circle]

∴ ∠OCB = ∠OBC = ∠ABC = ∠CBA = 50°.

∠AOC = ∠OCB + ∠OBC [∵ ∠AOC is exterior angle of ΔOCB]

∴ ∠AOC = 50° + 50° = 100°

And in ΔOCA, OC = OA [∵ Radius of the same circle]

∴ ∠OCA = ∠OAC = $\frac{1}{2}$ (180° - ∠AOC) = $\frac{1}{2}$ (180° - 100°) = 40°

∴ ∠CAB = ∠CAO = ∠OAC = 40°.