Prove that US is a tangent to circle PWUT at U.

Here's a step-by-step solution for Question 10.

Question 10.1: Prove that US is a tangent to circle PWUT at U.

Step 1: Identify relevant properties from the given information.
We are given that WPTU is a cyclic quadrilateral and $UW = UT$.
From $UW = UT$, $\triangle WUT$ is an isosceles triangle, which means the angles opposite these sides are equal:

$$\angle UW T = \angle UTW \quad (\text{angles opposite equal sides})$$

Step 2: Use the property of parallel lines.
We are given $SU \parallel WT$.
Therefore, the alternate interior angles are equal:

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