2021 JMPSC Invitationals Problems/Problem 12
Revision as of 17:35, 11 July 2021 by Samrocksnature (talk | contribs) (→Solution 1 (Clever Construction))
Problem
Rectangle is drawn such that
and
.
is a square that contains vertex
in its interior. Find
.
Solution 1 (Clever Construction)
We draw a line from to point
on
such that
. We then draw a line from
to point
on
such that
. Finally, we extend
to point
on
such that
.
Next, if we mark as
, we know that
, and
. We repeat this, finding
, so by AAS congruence,
. This means
, and
, so
. We see
, while
. Thus,
~Bradygho
See also
- Other 2021 JMPSC Invitationals Problems
- 2021 JMPSC Invitationals Answer Key
- All JMPSC Problems and Solutions
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.