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Hence` angle PRQ=pi//2` and points P, Q, R lie on the circle with PQ as diameter. <br> Also, `PQ=5.` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_CAL_C01_E17_003_S01.png" width="80%"> <br> Now, the maximum area of the triangle is <br> `Delta_(max)=(1)/(2)(5)((5)/(2))=6.25` <br> For area = 5, we have four symmetrical positions of point R (shown as `R_(1), R_(2),R_(3), R_(4)`). <br> For area = 6.25, we have exactly two points. <br> For area = 7, no such points exist.