TOT 1999 Autumn OJ1 folding a right triangle
Source:
May 11, 2020
geometryright trianglefoldingratioarea
Problem Statement
A right-angled triangle made of paper is folded along a straight line so that the vertex at the right angle coincides with one of the other vertices of the triangle and a quadrilateral is obtained .
(a) What is the ratio into which the diagonals of this quadrilateral divide each other?
(b) This quadrilateral is cut along its longest diagonal. Find the area of the smallest piece of paper thus obtained if the area of the original triangle is . (A Shapovalov)