Circumcentre

Q. The mid point of hypotenuse of a right angled triangle is equidistant from all the vertices of the triangle.

1. True
2. False

Q. If a line makes an angle of ${30}^{\circ }$ with the positive direction of $y-$ axis measured in anticlockwise direction, then the slope of the line is

1. $\sqrt{3}$
2. $-\sqrt{3}$
3. $\frac{1}{\sqrt{3}}$
4. $-\frac{1}{\sqrt{3}}$

Q. Circumcentre of a triangle, which is formed by the lines y=x, y=2x and y= 3x+4 is

1. (6, 8)
2. (6, -8)
3. (3, 4)
4. (-3, -4)

Q. If $S$ is the circumcentre of $△ABC$, where $A=(1,3),B=(-3,5),C=(5,-1)$, then

1. coordinates of $S$ will be $(-8,-10)$
2. coordinates of $S$ will be $(-4,-5)$
3. radius of circumcircle will be $5\sqrt{10}$ units
4. radius of circumcircle will be $5\sqrt{5}$ units

Q. The mid point of hypotenuse of a right angled triangle is equidistant from all the vertices of the triangle.

1. True
2. False

Q. Consider a right angled triangle $ABC$


If the sides of the triangle are $a=6,b=10,c=8$ units, then the distance between incentre and circumcentre will be

1. $2$
2. $\sqrt{3}$
3. $\sqrt{5}$
4. $3$

Q. $A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)$ are the vertices of a triangle. If P (x, y) is the circumcentre of the triangle, then
PA=PB=PC

1. True

2. False

Q. If $A=(6,0),B=(0,8),$ and the circumcenter of the $△OAB$ where $O$ is the origin, is $(\alpha ,\beta ),$ then the value of $\alpha +\beta$ is

Q. If a line makes an angle of ${30}^{\circ }$ with the positive direction of $y-$ axis measured in anticlockwise direction, then the slope of the line is

1. $\sqrt{3}$
2. $-\sqrt{3}$
3. $\frac{1}{\sqrt{3}}$
4. $-\frac{1}{\sqrt{3}}$

Q. Consider a right angled triangle $ABC$


If the sides of the triangle are $a=6,b=10,c=8$ units, then the distance between incentre and circumcentre will be

1. $2$
2. $\sqrt{3}$
3. $\sqrt{5}$
4. $3$

Q. The slope of the line passing through points $(3,2)$ and $(2,5)$ is

1. $\frac{1}{3}$
2. $-3$
3. $-\frac{1}{3}$
4. $3$

Q. The circumcentre of the triangle formed by $(2,-5),$ $(2,7),$ $(4,7)$ is

1. $(3,1)$
2. $(2,7)$
3. $(3,-1)$
4. $(-3,-1)$

Q. Consider a right angled triangle $ABC$


If the sides of the triangle are $a=6,b=10,c=8$ units, then the distance between incentre and circumcentre will be

1. $2$
2. $\sqrt{3}$
3. $\sqrt{5}$
4. $3$

Q. $A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)$ are the vertices of a triangle. If P (x, y) is the circumcentre of the triangle, then
PA=PB=PC

1. True

2. False

Q. $A(x_1,y_1),B(x_2,y_2),C(x_3,y_3)$ are the vertices of a triangle. If P (x, y) is the circumcentre of the triangle, then
PA=PB=PC

1. True

2. False