Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem A. 781. (September 2020)

A. 781. We want to construct an isosceles triangle using a compass and a straightedge. We are given two of the following four data: the length of the base of the triangle (\(\displaystyle a\)), the length of the leg of the triangle (\(\displaystyle b\)), the radius of the inscribed circle (\(\displaystyle r\)) and the radius of the circumscribed circle (\(\displaystyle R\)). In which of the six possible cases will we definitely be able to construct the triangle?

Proposed by György Rubóczky, Budapest

(7 pont)

Deadline expired on October 12, 2020.

Statistics:

39 students sent a solution.

7 points: Lovas Márton.

6 points: Arató Zita.

5 points: 3 students.

4 points: 5 students.

3 points: 1 student.

2 points: 21 students.

1 point: 5 students.

0 point: 2 students.

Problems in Mathematics of KöMaL, September 2020

39 students sent a solution.
7 points:	Lovas Márton.
6 points:	Arató Zita.
5 points:	3 students.
4 points:	5 students.
3 points:	1 student.
2 points:	21 students.
1 point:	5 students.
0 point:	2 students.