$A$, $D$, $E$ and $F$ are points on the circle such that $AD = ED$. $ADB$, $AEC$

Question

$A$, $D$, $E$ and $F$ are points on the circle such that $AD = ED$. $ADB$, $AEC$ and $DFC$ are straight lines and $CD$ bisects $\angle BCE$. $\angle BED = 34^\circ$ and $\angle BFC = 124^\circ$. Prove that $AB$ is perpendicular to $CD$, $BCED$ is a cyclic quadrilateral. Describe clearly another circle that will pass through $A$, $C$ and $D$. As shown in the diagram, $B,E,F$ are collinear, with $F$ between $B$ and $E$.

Accepted Answer

Proved: (a)(i) $AB\perp CD$ (a)(ii) $BCED$ is cyclic (b) The circle with diameter $AC$ passes through $A$, $C$ and $D$

IP2U14 HOT Q1

IP2U14 HOT Q1

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