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Mean Geometrically

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

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Golden Triangle

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.

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Sangaku

The square ABCD is split into three triangles by the lines BP and CP. Find the radii of the three inscribed circles to these triangles as P moves on AD.

So Big

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What can you say about the tangents of the angles at the centre of the circle?

Alternatively, can you see how you might calculate the area of these 6 smaller triangles?