MathematicsIf A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the center of the circle through A, B and C.

If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is the center of the circle through A, B and C.

A
True
B
False.

Solution:

Given that,

A, B, C, D

are four points such that

∠ B A C = 30 °, ∠ B D C = 60 °

Since, in a circle there can be many points D, for which

∠ B A C = 30 °, ∠ B D C = 60 °

And from those points each point will not be the center of the circle, thus the statement is false.
If A, B, C, D are four points such that ∠BAC = 30° and ∠BDC = 60°, then D is not the center of the circle through A, B and C.
Hence, option 2 is correct.