perplexus.info :: Geometry : Square and triangle on centers

Square and triangle on centers (Posted on 2022-03-17)

Consider unit equilateral Triangle ABC with center O and unit square DEFG with center O' where O is on segment DE and O' is on segment AB.

If O' and A coincide, find the area of overlap of the triangle and square.

If O' is not at A (but closer to A than B), find the largest possible distance O'A.
When this distance occurs, find the area of overlap.

No Solution Yet Submitted by Jer

Rating: 4.0000 (1 votes)

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soln

Comment 1 of 1

For Part A, The triangle's bisector is parallel to DE and

the overlap is 0.1778 sq. units.

See Part A solution.

For Part B, O'A is maximized when O'O lies along the square's bisector, giving O'A = 0.09175 and an overlap area of 0.193 sq. units.

Edited on March 19, 2022, 5:18 pm

Posted by Steven Lord on 2022-03-19 08:23:53

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