JEE MAIN - Mathematics (2021 - 20th July Evening Shift - No. 18)
Consider a triangle having vertices A($$-$$2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC, bisects line BC, and intersects y-axis at point $$\left( {0,{\alpha \over 2}} \right)$$, then the value of real number $$\alpha$$ is ________________.
Answer
9
Explanation
$${\left( {\sqrt {50} } \right)^2} = {\left( {\sqrt {45} } \right)^2} + {\left( {\sqrt 5 } \right)^2}$$
$$\angle B = 90^\circ $$
Circum-center $$ = \left( {{1 \over 2},{{11} \over 2}} \right)$$
Mid point of BC $$ = \left( {2,{{17} \over 2}} \right)$$
Line : $$\left( {y - {{11} \over 2}} \right) = 2\left( {x - {1 \over 2}} \right) \Rightarrow y = 2x + {9 \over 2}$$
Passing through $$\left( {0,{\alpha \over 2}} \right)$$
$${\alpha \over 2} = {9 \over 2} \Rightarrow \alpha = 9$$
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