Straight LineHardBloom L3
Question
$A,B$ and $C$ are points in the $xy$-plane such that $A(1,2);B(5,6)$ and $AC = 3BC$. Then :
Options
A.$ABC$ is a unique triangle
B.There can be only two such triangles.
C.No such triangle is possible
D.There can be infinite number of such triangles.
Solution
Sol. [Key Concept: With $B$ fixed and $AC = 3$, the triangle-existence constraints decide how many positions of $C$ are possible.]
Locus of $C$ is a circle.
⇒ infinite $\bigtriangleup ABC$ can be formed
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