JAMB 1995 · UME · Q27

$PT$ is a tangent to the circle $TYZX$ , $YT = YX$ and $\angle PTX = 50^\circ$ . Calculate $\angle TZY$ .

Worked solution (try it first)

The angle between tangent $TP$ and chord $TX$ equals the angle in the alternate segment, so $\angle TYX = \angle PTX = 50^\circ$ .
$YT = YX$ , so triangle $TYX$ is isosceles: $\angle YXT = \dfrac{180^\circ - 50^\circ}{2}$
$= 65^\circ$ .
Angles in the same segment are equal.
$\angle TZY$ and $\angle TXY$ both stand on arc $TY$ , so $\angle TZY = 65^\circ$ , option B.