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This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?

# Ice Cream Tangent

##### Stage: 4 Short Challenge Level:

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

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.
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