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And counting

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?

Scroll down for a solution to this problem.

Solution

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

Solution by Ferdi Yılmaztürk.

Spin-off

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

A pattern is emerging by uila.

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

Theorem by Jan.
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