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In the diagram below, two circles intersect at $\mathrm{K}$ and $\mathrm{Y}$. The larger circle passes through $\mathrm{O}$, the centre of the smaller circle. $\mathrm{T}$ is a point on the smaller circle such that $\mathrm{KT}$ is a tangent to the larger circle. TY produced meets the larger circle at W. WO produced meets $\mathrm{KT}$ at $\mathrm{E}$.
Let $\hat{\mathrm{W}}_{1}=x$

1. Determine FOUR other angles, each equal to $x$.
$2. \quad$ Prove that $\hat{T}=90^{\circ}-x$.
$3. \quad$ Prove that $\mathrm{KE}=\mathrm{ET}$.

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