A triangle containing an altitude and the inscribed circle. One tangency point is shown. The red line segments have equal length. What is the proportion of the triangle sides a : b : c?

Solution

The sides have proportion a : b : c = 5 : 6 : 7.

Spin-off

Following the publication of this puzzle on Twitter, mathematician uila discerned an interesting pattern in triangles having sides of consecutive integer length.

This pattern was generalized by mathematician Jan to the following theorem.