In the figure, AB is diameter of a circle with centre O and QC is a tangent to the circle at C. If angle CAB= 30degree, find 1. angle CQA 2. angle CBA.
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posed: AB is the diameter of a circle with center O and QC is a tangent to the circle at C. If angle CAB=30 degrees then what is the angle CQA and CBA?
The diagram below is hopefully a correct interpretation of the info given in the problem. ▵ABC with the circle’s diameter as one of its sides will always be right-angled, so ∠CBA is an easy 60⁰.
∠CQA is not as easy, as the position of Q has not be specified uniquely. In my diagram I have shown 3 arbitrarily placed “Q’s”, and ∠CQA would have three different values for each location of Q.
Perhaps there was a typo on the angle name? Was it supposed to be ∠QCA? (That would reduce the possible values to just 2.)
Hope this helps! Cheers! :)
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