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8 Methods for Three by One

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Ice Cream Tangent

Stage: 4 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
See all short problems arranged by curriculum topic in the short problems collection

The diagram shows a semi-circle and an isosceles triangle which have equal areas.
What is the value of $\tan x^{\circ}$?

Diagram

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.