In the diagram below, $TAX$ and $TCY$ are tangents to the circle at $A$ and $C$ respectively

Question

In the diagram below, $TAX$ and $TCY$ are tangents to the circle at $A$ and $C$ respectively. $AC$ meets $TD$ at $E$. $D$ is on $BC$ such that $TD$ is parallel to $AB$. Prove that angle $\angle ACB$ is equal to angle $\angle ATD$.[2] Explain why a circle can be drawn passing through the points T,A,D and C.[1] Hence prove that $CE \times AE = DE \times TE$[3]

Accepted Answer

(i) $\angle ACB=\angle ATD$. (ii) $T,A,D,C$ are concyclic. (iii) $CE\times AE=DE\times TE$.

(A Math) 2025 CCHY PRELIMS P1 Q6

(A Math) 2025 CCHY PRELIMS P1 Q6

Solution:

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