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Question

ABCD is a quadrilateral such that A is the centre of the circle passing through B, C and D. Which one of the following options is correct?

A
CBD+CDB=BAD
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B
CBD+CDB=12BAD
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C
CBD+CDB=23BAD
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D
CBD+CDB=34BAD
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Solution

The correct option is B CBD+CDB=12BAD

Given that ABCD is a quadrilateral such that A is the centre of the circle passing through B, C and D. Join AC.



Since angle subtended by an arc at the centre is double the angle subtended by it at point on the remaining part of the circle,

CAD=2×(CBD)(1) and
BAC=2×(CDB)(2).

Adding (1) and (2), we get
CAD+BAC=2(CBD+CDB)
BAD=2(CBD+CDB)
Hence, CBD+CDB=12BAD.


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