$A$, $B$, $C$, $D$ and $E$ are points on a circle. $AE=AB$, $AE$ is parallel to $BD$

Question

$A$, $B$, $C$, $D$ and $E$ are points on a circle. $AE=AB$, $AE$ is parallel to $BD$, angle $BEC=22^\circ$ and angle $EAC=80^\circ$. Find angle $AEB$.[2] Find angle $DEC$.[3] Angle $AFE=78^\circ$. Determine the position of point $F$. Justify your answer.[2]

Accepted Answer

(a) $39^\circ$. (b) $41^\circ$. (c) Underdetermined: the centre is one possible position, but $\angle AFE=78^\circ$ alone does not determine $F$.

2025 CGS PRELIMS P2 Q3

2025 CGS PRELIMS P2 Q3

Solution:

Solution locked