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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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So Big

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

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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.

Vecten

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

See the solution to part (1) from Aurel of King Edward VI School Southampton.

The question is left open and solutions to the other parts will be welcomed. Any small item that you discover is worth sharing and all results will be published.

Possible support
See the problem Square-areas