MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Circle Theorems
Problem
A circle has diameter XY. A point Z is any point on the circumference different from X and Y. Another point W is chosen on the circumference on the same side of XY as Z. Answer the following.
(i) State the special name of triangle XYZ and give a reason for your answer.
(ii) Compare ∠XZW and ∠XYW. Justify your conclusion.
(iii) Write a short explanation, in not more than five lines, to show why the result in part (i) holds for every position of Z on the circle.