WMC 2018 Senior Problem 1

Level 1

A circle is circumscribed about an isosceles right triangle whose leg (short side) has length 5 5 . What is the circumference of the circle?

5 π 2 5\pi\sqrt { 2 } 13 π 2 \frac { 13\pi }{ 2 } 5 π 2 2 \frac { 5\pi \sqrt { 2 } }{ 2 } 13 π 13\pi 5 π 5\pi

Tiger Ang by Tiger Ang , 20, Malaysia

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1 solution

Julian Yu
Oct 10, 2018

The hypotenuse of a right angled triangle is a diameter of its circumcircle. The hypotenuse has length 5 2 5\sqrt{2} , so the circumference of the circle is π d = 5 2 π \pi d=5\sqrt{2}\pi .

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