QuestionA, B, C and D are four points on the circumference of a circle. TA is the tangent to the circle at A. Angle DAT $=30^{\circ}$. Angle $\mathrm{ADC}=132^{\circ}$. a) Calculate the size of angle ABC . Explain your method: b) Calculate the size of angle CBD. Explain your method. c) Explain why AC cannot be a diameter of the circle.

Studdy Solution
For AC to be a diameter, $\angle ABC$ would have to be $90^\circ$ (since the angle subtended by a diameter is a right angle). However, we calculated $\angle ABC = 48^\circ$, which is not $90^\circ$. Hence, AC cannot be a diameter.
The solutions are: a) $\angle ABC = 48^\circ$ b) $\angle CBD = 30^\circ$ c) AC cannot be a diameter because $\angle ABC$ is not $90^\circ$.