Products Determined by a Point on the Circumcircle

PA

≈

13.59

PA'

≈

2.71

R

≈

7.21

PQ

≈

2.55

PA

×

PA'

≈

36.79

2

R

×

PQ

≈

36.79

Let ABC be a triangle and P be a point on the circumcircle of circumradius

R

. Let A' and B' be the perpendicular projections of P onto BC and CA, respectively. Let Q be the perpendicular projection of P onto A'B'. Then

PA×PA'=2

R

×PQ

.

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