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Question

A(1,2) and B(7,10) are two points. If P(x,y) is a point such that APB=60 and area of ΔAPB is maximum, then which of the following is (are) TRUE ?

A
P lies on any line perpendicular to AB
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B
P lies on the perpendicular bisector of AB
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C
P lies on the line 3x+4y=36
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D
Radius of circumcircle of ΔPAB is 10 units
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Solution

The correct options are
B P lies on the perpendicular bisector of AB
C P lies on the line 3x+4y=36
Equation of perpendicular of AB is
yy1=m(yy1)
y6=34(x4)
3x+4y=36
Also, AB=10,AL=5
Therefore, AH= radius of circle=103=ALcosec60 and AL perpendicularly bisect the AB.

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