Review question

# Can we find the areas within the semicircles? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6699

## Question

State the theorem of Pythagoras concerning the three sides of a right-angled triangle.

The diagram shows an isosceles triangle $ABC$ right-angled at $B$. Semicircles $S_1$ and $S_2$ are drawn on $AB$ and $AC$ as diameter, as shown.

1. Explain why $S_2$ passes through $B$.
2. If $AB = \quantity{2x}{cm}$, show that the area shaded vertically is $\quantity{\tfrac{1}{2}(\pi - 2)x^2}{cm^2}$.
3. Prove that the area shaded horizontally is half the area of the triangle $ABC$.