perplexus.info :: Geometry : Rectangular distance problem

Rectangular distance problem (Posted on 2025-04-23)

The point P lies on side CD of rectangle ABCD, with CD = 20 and AD = 10. The circumcircle ω of △ABP re-intersects CD at Q. Given that the radius of ω is 11, find the distance PQ.

No Solution Yet Submitted by Danish Ahmed Khan

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Simple solution

| Comment 3 of 6 |

Let M be the midpoint of AB, N be the midpoint of CD. Call the circumcenter of the circle W. W is on MN.

On right triangle BMW, BM=10, BW=11, MW=sqrt(21).

On right triangle PWQ, PW=11,NW=10-sqrt(21).

PN=sqrt(20-sqrt(21)).

PQ=2*sqrt(20sqrt(21))

=4*525^(1/4).

Posted by Jer on 2025-04-27 12:24:35

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