In the diagram, $A$, $B$, $C$ and $D$ are points on the circumference of the circle centre \

Question

In the diagram, $A$, $B$, $C$ and $D$ are points on the circumference of the circle centre $O$. $ABE$ and $DCE$ are straight lines and $ST$ is a tangent to the circle at $A$. $ST$ is parallel to $DE$, $\angle CEB=36{}^\circ$ and $\angle DAB=83{}^\circ$. Calculate angle $OAB$, angle $ABC$, angle $AOD$. Show that $ACD$ is an isosceles triangle.

Accepted Answer

(a)(i) $54^\circ$ (a)(ii) $119^\circ$ (a)(iii) $122^\circ$ (b) Proved: $\triangle ACD$ is isosceles

Investigating Geometric Proofs through Circle Angle Invariants

Investigating Geometric Proofs through Circle Angle Invariants

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