Easy Coordinate Geometry

Level pending

A triangle ABC is inscribed in the circle $x^2 + y^2 = 25$ .

Given : $A ( 3 , 4 )$ and $B ( -4 , 3 )$ ,

Find the angle $BCA$

pi/2 None of these pi/4 pi/3

1 solution

Md Sarwar
Feb 14, 2014

given equation is a circle with radius=5,draw this circle and plot the given points i.e. B(-4,3)&A(3,4)..join AB=5√2.Take any point C on circle and join CA & CB.....from origin(O) join OA=OB=OC=5. In /\ OAB, OA=OB=5 AB=5√2 means /\OAB is isosceles with angle 90 at O now from property of circle..which states that if a triangle is inscribed in a circle then angle subtended by centre to the vertices is double of angle subtended by 3rd vertex to the same vertices... using above property angle BOA=90 or pi/2 angle BCA=45 or pi/4

The intended solution is somewhat the same.

If you join $OA$ and $OB$ clearly they are perpendicular since their slopes are negative reciprocals. The rest as you rightly pointed follows giving the angle $BCA = pi/4$ .

Leon Fernandes - 7 years, 3 months ago

Easy Coordinate Geometry

1 solution

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