Circle through 3 Points

Q. Angles in the same segment of a circle are

1. 
   Complementary
2. 
   Supplementary
3. 
   Equal
4. 
   Vertically opposite angles

Q.

Draw a circle with diameter $6cm$ and measure the length of the radius of the circle drawn.

Q. Let ABC be an equilateral triangle. The bisector of $\angle$ BAC meets the circumcircle of ABC in D. Suppose DB + DC = 4. The diameter of the circumcircle of triangle ABC is

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

Q. Let ABC be an equilateral triangle. The bisector of ∠BAC meets the circumcircle of ABC in D. Suppose DB + DC = 4. The diameter of the circumcircle of triangle ABC is

Q. In the given figure, O is the centre of the circle with radius 7 cm. If OC = CD, then the length of chord AB is

1. 
   $3.5\sqrt{3}cm$
2. 
   $7\sqrt{5}cm$
3. 
   $7\sqrt{3}cm$
4. 
   $14cm$

Q. A straight line is drawn cutting two equal circles and passing through the midpoint M of the line joining their centres O and O’. Prove that chords AB and CD, which are intercepted by the two circles are equal.

Q. In the given figure, O is the centre of the circle. If $\angle PQR={130}^{\circ }$ , then the measure of $\angle RPT$ is

1. 
   ${50}^{\circ }$
2. 
   ${30}^{\circ }$
3. 
   ${45}^{\circ }$
4. 
   ${40}^{\circ }$

Q.

Given three points, is it possible to construct a circle with all three on its circumference?

1. Only if they are non-collinear.

2. Only if they are in the same plane.

3. Only if they are concentric.

4. It is not possible.

Q.

How many circles can be drawn circumscribing a given triangle?

1. infinite

2. 1

3. 2

4. 3

Q. 4. A chord PQ of a circle is parallel to the tangents drawn at a point R of the circle. Prove that R bisects the arc PRQ

Q.

ABC, DBC are two triangles in which AC and BD meet at X.
If AX = DX and BX = CX, then which of the following statements are correct?

1. $\Delta AXB\cong \Delta DXC$ by ASA postulate

2. $\Delta AXB\cong \Delta DXC$ by SAS postulate

3. $\angle BAX=\angle CDX$

4. $AB=CD$

Q. Through three collinear points, the number of circles that can be drawn passing through all the points is/are

1. one
2. two
3. three
4. none of these

Q.

Through three collinear points a circle can be drawn. Write True or False and justify your answer in each of the following:

1. True
2. False

Q.

How many circles can be drawn passing through 3 non-collinear points ?

1. Infinite

2. 1

3. 0

4. 4

Q.

Let $\mathrm{P}$ and $\mathrm{Q}$ be the center of two circles of equal radii, draw them so that each one of them passes through the center of the other. let them intersect at $\mathrm{M}$ and $\mathrm{N}$ examine whether $\overline{PQ}\perp \overline{MN}$

Q.

How many circles can be drawn passing through three collinear points?

1. 1

2. 0

3. 2

4. Infinite

Q.

Diameter divides the circle into ………. semicircles.

Q. Drawn different pairs of circle. How many point does each pair have in common ?

Q.

Choose the correct answer

A diameter divides a circle into_______

1. Sectors

2. Semicircles

3. Arcs

4. Tangents

Q.

How many circles can be drawn circumscribing a given triangle?

1. 1

Q. Using the information given in the figure, BC = 4 cm

1. True
2. False

Q.

There are three points given on a plane. How many circles can be drawn passing through all three points?

1. 1

2. 3

3. 0

4. Data inadequate

Q. Draw a circle with centre C and radius 3.4 cm. Draw any chord $\overline{AB}.$ Construct the perpendicular bisector of $\overline{AB}$ and examine if it passes through C.

Q.

In the following figures, are the centre of the circle and the circumcentre of the triangle the same?

1. Yes, Yes

2. No, No

3. Yes, No

4. No, Yes

Q.

In Figure, if $ OA=5 cm$, $ AB=8 cm$ and $ OD$ is perpendicular to $ AB$, then $ CD$ is equal to:

(4)

Q.

Given three points, is it possible to construct a circle with all three on its circumference?

1. Only if they are concentric.

2. It is not possible.

3. Only if they are non-collinear.

4. Only if they are in the same plane.

Q. Using the information given in the figure, BC = 4 cm

1. True
2. False

Q.

ABC is a triangle. Number of circles that can be drawn circumscribing the triangle is/are ?

1. 2
2. 3

3. 0

4. 1

Q.

How many circles can be drawn passing through 3 non-collinear points ?

1. Infinite

2. 1

3. 0

4. 4

Q.

In the following figures, are the centre of the circle and the circumcentre of the triangle the same?

1. Yes, Yes

2. No, Yes

3. No, No

4. Yes, No