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Question

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

A
sometimes true
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B
false
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C
true
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D
none of the above.
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Solution

The correct option is A sometimes true
GivenA,B,C&DarefourpointssuchthatBAC=30o&BDC=60o.TofindoutifDisthecentreofthecirclewhichpassesthroughA,B&C.SolutionBAC=30o&BDC=60o.BDC=2BAC.Weknowthattheanglesubtendedbyachordatthecentreofacircleisdoubletheangleatthecircumferencesubtendedbythesamechord.BDCistheangleatthecentreandBACistheangleatthecircumferencesubtendedbythechordBC.SoDisthecentreofthecirclewhichpassesthroughA,B&C.ThestatementiscorrectbyfigIButbyfigIIthisisnottrue.Sothestatementisnotalwaystrue.AnsOptionA.
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