perplexus.info :: Geometry : More Tangential Trapezoids

More Tangential Trapezoids (Posted on 2022-12-16)

In A Tangential Trapezoid, Jer describes a specific isosceles tangential trapezoid. I am going to generalize that idea.

How many isosceles tangential trapezoids exist where all their sides and diagonals are whole numbers and all those dimensions are at most 1000?

An example is a trapezoid with bases 6 and 20, lateral sides of 13, and diagonals of 17.

Bonus challenge: How many of these trapezoids have all dimensions at most 100,000?

No Solution Yet Submitted by Brian Smith

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re: computer solution (hope it's right--see caveats)

| Comment 2 of 4 |

(In reply to computer solution (hope it's right--see caveats) by Charlie)

The same number, 85, is gotten when

if abs(round(d)-d)<d/1e12

and

if abs(round(s)-s)<d/1e12

are substituted for the integral checks done by relying on sym() to provide the appropriate leeway.

This adds to my confidence in the answer.

Posted by Charlie on 2022-12-16 10:27:40

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