Circumcentre

Q. The point of intersection of the perpendicular bisectors of a triangle is called .

1. Incentre
2. Circumcentre
3. Centroid
4. Orthocentre

Q.

The locus of point equidistant from three vertices of a triangle is……………

__

Q. What is the locus of a point which is equidistant from a fixed reference point called?

1. Straight Line
2. circle
3. ellipse
4. hyperbola

Q.

A triangle has only one circumcircle and one incircle.

1. False

2. True

Q.

The circumcircle of a triangle passes through _____.

1. inside a triangle touching all its sides

2. one of the vertices of a triangle

3. all the vertices of a triangle

4. two vertices of a triangle

Q.

The number of circles that can be drawn, touching all the vertices of a triangle is ___ .

1. Two

2. Many

3. None of these

4. One

Q. What is the locus of a Circle

Q. A circle is drawn through the vertices P, Q and R of a triangle PQR with PQ = 52 cm, QR = 56 cm and PR = 60 cm as shown in the given figure. Find the diameter of the circle.

Q.

Describe the locus for questions 1 to 13 given below:

the locus of points inside a circle and equidistant from two fixed points on the circumference of the circle.

Q. The point of intersection of the perpendicular bisectors of a triangle is called:

1. in-centre
2. circumcentre
3. orthocentre
4. centroid

Q.

The locus of a point, equidistant from two given points, is the __ of the line segment joining the two points.

Q.

If the source is opposite to the direction of the sun, then honey bees will convey the direction by

1. Clockwise round dance

2. Upright down tail wagging dance

3. Anti-clockwise round dance

4. None of these

Q. Find the coordinates of the circumcenter of a triangle whose vertices are (8, 6), (8, – 2) and (2, – 2). What is the circumradius of this triangle?

Q. The radii of the escribed circles of triangle ABC are r_a, r_{b } and r_c respectively. If r_a+r_c = 3R and r_b +r_c =2Rthen the smallest angle of the triangle is (where R is the circuradius of triangle ABC)

Q.

Describe the locus for questions 1 to 13 given below:

The locus of a point P, so that:

$A{B}^2=A{P}^2+B{P}^2$

where A and B are two fixed points.

Q.

A semicircle is constructed outwards on side BC of a triangle ABC as on the diameter. Given points K and L that divide the semicircle into 3 equal arcs, prove that lines AK and AL divide BC into 3 equal parts.

Q.

For a triangle PQR, if the circumcenter is C. Will triangle PQT also have the same circumcenter if T is another point on the circumcircle?

1. False

2. True

Q. If the line through $A(-2,6)$ and $B(4,8)$ is perpendicular to the the line through the points $C(8,12)$ and $D(x,24),$ then the value of $x$ is:

1. $2$
2. $4$
3. $1$
4. $8$

Q.

The speed of sound is 332 metres per second.A gun is fired.Describe the locus of all the people on the earth's surface, who hear the sound exactly after one second?

Q.

The locus of a point equidistant from three vertices of a triangle is the

1. the incentre of the triangle

2. any side

3. the orthocentre of the triangle

4. the circumcentre of the triangle

Q.

The locus of a point, equidistant from two given points, is the __ of the line segment joining the two points.

Q. A semi-circle is inscribed in a triangle such that its diameter is on the hypotenuse, then the triangle is?

Q. Question $1$: Line $AB$ contains points $A(0,1)$ and $B(1,5)$. The slope of line $AB$ is ... ? $

Q.

What exactly deos the foci of an ellipse mean? What is its value in case of a circle and why?

Q. Slope of the line $AB$ is $-\frac{4}{3}$. Co-ordinates of points $A$ and $B$ are $(x,-5)$ and $(-5,3)$ respectively. What is the value of $x$

1. $-1$
2. $2$
3. $-2$
4. $1$

Q.

two buildings are 3.3km apart. a gun is fired from one building. the difference between the seeing the flash of gun and its sound is 10s. find the speed of sound in air

Q. Which of the following statements is/are correct statements?
1. Centroid of a triangle is the point of concurrency of medians
2. Incentre of a triangle is the point of concurrency of perpendicular bisectors of the sides of the triangle
3. Circumcentre of a triangle is the point of concurrency of internal bisectors of the angles of the triangle
4. Orthocentre of a triangle is the point of concurrency of altitudes of the triangle drawn from one vertex to opposite side
5. A triangle can have only one excentre

1. All 1, 2, 3, 4, 5
2. only 1, 4, 5
3. only 1, 2, 3, 4
4. only 1, 4