question_answer

Consider a \[\Delta ABC\] whose vertices are

\[A=(3+4\cos \theta ,-5+4\sin \theta )\],

\[B=\left( 3+4\cos \left( \theta +\frac{2\pi }{3} \right),-5+4\sin \left( \theta +\frac{2\pi }{3} \right) \right)\]

\[C=\left( 3+4\cos \left( \theta +\frac{4\pi }{3} \right),-5+4\sin \left( \theta +\frac{4\pi }{3} \right) \right)\]

STATEMENT-1: The orthocenter of the triangle is (3, -5).

STATEMENT-2: The triangle ABC is equilateral.

A)  Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement- 1.

B)  Statement-2 is true, Statement-2 is true and Statement-2 is NOT correct explanation for statement-1.

C)  Statement-1 is true, Statement-2 is false.

D)  Statement-1 is false, Statement-2 is true.

Correct Answer: A

Solution :

\[\Delta \,ABC\]is equilateral and its circumcenter is (3, -5) and circumradius is 4.