Consider a triangle having vertices A(-2,3), B(1,9) and C(3,8). I… - Vidyadip

MCQ

Consider a triangle having vertices $A(-2,3), B(1,9)$ and $C(3,8)$. If a line $L$ passing through the circum-center of triangle $\mathrm{ABC}$, bisects line $\mathrm{BC}$, and intersects $\mathrm{y}$-axis at point $\left(0, \frac{\alpha}{2}\right)$, then the value of real number $\alpha$ is $.....$

A
$81$
B
$3$
✓
$9$
D
$45$

✓

Answer

Correct option: C.

$9$

c
$(\sqrt{50})^{2}=(\sqrt{45})^{2}+(\sqrt{5})^{2}$

$\angle \mathrm{B}=90^{\circ}$

$\text { Circum-center }=\left(\frac{1}{2}, \frac{11}{2}\right)$

Mid point of $B C=\left(2, \frac{17}{2}\right)$

Line $:\left(y-\frac{11}{2}\right)=2\left(x-\frac{1}{2}\right) \Rightarrow y=2 x+\frac{9}{2}$

Passing through $\left(0, \frac{\alpha}{2}\right)$

$\frac{\alpha}{2}=\frac{9}{2} \Rightarrow \alpha=9$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 9. straight line→9. straight line — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The eccentricity of ellipse $(x-3)^2 + (y -4)^2 = \frac{y^2}{9} +16 ,$ is -

The value of $\cos52^\circ+\cos68^\circ+\cos172^\circ\text{ is }$

A circle with center (3, 8) contains the point (2, -1). Another point on the circle is:

Choose the correct answer. The following information relates to a sample of size 60 $\sum\text{x}^2=18000$ and $\sum\text{x}=960,$ then the variance is:

Consider the set of all $7-$digit numbers formed by the digits $0,1,2,3,4,5,6$, each chosen exactly once. If a number is randomly drawn from this set, the probability that it is divisible by $4$ is

If $log_ab + log_bc + log_ca$ vanishes where $a, b$ and $c$ are positive reals different than unity then the value of $(log_ab)^3 + (log_bc)^3 + (log_ca)^3$ is

If $x + \frac{1}{x} = 2\cos \alpha $, then ${x^n} + \frac{1}{{{x^n}}} = $

Mean of twenty observations is 15. It two observations 3 and 14 are replaced by 8 and 9 respectively, then the new mean will be:

The numbers of permutations of $n$ things taken $r$ at a time, when $p$ things are always included, is

If $x,\;y,\;z$ are in $G.P.$ and ${a^x} = {b^y} = {c^z}$, then