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Question 10
Write True or False and justify your answer :

In the figure, if AOB is a diameter and ADC=120, then CAB=30.

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Solution

True

Join CA and CB

Since ADCB is a cyclic quadrilateral,
ADC+CBA=180 [sum of opposite angles of cyclic quadrilateral is 180]
CBA=180120=60 [ ADC=120]

In ΔCAB, ABC+ACB=180 [by angle sum property of a training]
CAB+60+90=180 [triangle formed from diameter to the circle is 90 i.e., ACB=90]
CAB=180150=30


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