Dear friends and visitors of the site,
Welcome to a New Year and new problems!
Here is the January Problem:
Vertices A and C of a solid triangle ABC (with a right angle B)
are sliding along the sides of another right angle.
What is the locus of the vertex B ?
Answer Submission Is Not Available
Dear visitors of the site!
Thank you for you numerous solutions.
The first one to send correct solutions were Andy and Gina.
Our congratulations to them!Here is my solution:
Quadrilateral AOBC is concyclic (AC is seen at the right angle from B and from O).Thus, angles BOC and BCA are equal.
Hence, p. B moves along the fixed line BO with the gradient equal to tan(angle BAC).
A more detailed analysis can define the limits for p. B.
Thank you and try the February Problem!