perplexus.info :: Geometry : Locus in quarter

Locus in quarter (Posted on 2025-05-27)

Let P be a variable point on the circumference of a quarter-circle with radii OA, OB and ∠AOB = 90◦. H is the projection of P on OA. Find the locus of the incenter of the right-angled triangle HPO.

No Solution Yet Submitted by Danish Ahmed Khan

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a start

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https://www.desmos.com/calculator/fu9czr4xfg

I managed to come up with a parametric equation: line 11

It isn't very nice, though.

After playing around I managed to fit the arc of a circle with radius sqrt(2)/2 and centered half the radius from the midpoint of OA.

If I get a chance later, I'll try to show the two are equivalent.

Posted by Jer on 2025-05-28 10:22:18

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