Two congruent right triangles inscribed in a circle. The circle centre lies on one of the hypotenuses. What’s the angle?

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## Solution

The angle α is 67,5°.

Our solution follows these steps:

- Extend the hypotenuse through the centre to point G. Using the fact that β=90-α, it makes a right angle with CD.
- Using reflection symmetry in the line through AG, triangle ADC is seen to be isosceles with a top angle of 2β.
- Triangle ADE is also isosceles because of the congruency of AE and ED. It has a top angle of 90, so both other angles are 45.
- This gives 2β=45=180-2α, resulting in α=67,5.

## Visual solution

## Poem

The coloured toucan

Who knows a toucan?

May be you can

I’ll write about that bird I can

But don’t know so much

About toucan !

So it’s more important than

Just write about two toucans

I’m his real good fan

Living in the city of Lausanne

Where I have a plan

Write about a toucan