MathDB

5

Part of 2017 Auckland Mathematical Olympiad

Problems(2)

rectangles by lines // sides of rectangle (2017 Auckland MO J5)

Source:

11/14/2021
A rectangle ABCDABCD is given. On the side ABAB, n different points are chosen strictly between AA and BB. Similarly, mm different points are chosen on the side ADAD between AA and DD. Lines are drawn from the points parallel to the sides. How many rectangles are formed in this way?
An example of a particular rectangle ABCDABCD is shown with a shaded one rectangle that may be formed in this way. https://cdn.artofproblemsolving.com/attachments/e/4/f7a04300f0c846fb6418d12dc23f5c74b54242.png
combinatorial geometrycombinatoricsrectangle
<C wanted, AB = CH, orthocenter (2017 Auckland MO S5)

Source:

12/31/2020
The altitudes of triangle ABCABC intersect at a point HH.Find ∠ACB\angle ACB if it is known that AB=CHAB = CH.
geometryanglesorthocenter