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.
![](https://mirangu.com/wp-content/uploads/2022/02/AndCountingSolution.jpg)
Spin-off
Following the publication of this puzzle on Twitter, mathematician uila discerned an interesting pattern in triangles having sides of consecutive integer length.
![](https://mirangu.com/wp-content/uploads/2022/02/AndCountingUila.jpg)
This pattern was generalized by mathematician Jan to the following theorem.
![](https://mirangu.com/wp-content/uploads/2022/02/AndCountingJan.jpg)