Question

In the given figure, O is the centre of the circle. Determine $\angle APC$, if DA and DC are tangent and $\angle ADC={50}^{\circ }$

Answer 1

Since DA and DC are tangents, they are perpendicular to radii or OA and OC.
Hence, $\angle AOC=360-(90+90)-\angle ADC=180-50=130$.
$\angle APC=\frac{1}{2}$ Reflex ADC (As it is angle in other segment of chord AC)
$=\frac{1}{2}(360-130)=\frac{1}{2}\times 230=115degrees$.