# Circle through 3 Points

## Trending Questions

**Q.**Angles in the same segment of a circle are

Complementary

Supplementary

Equal

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 ∠ BAC meets the circumcircle of ABC in D. Suppose DB + DC = 4. The diameter of the circumcircle of triangle ABC is

- 4
- 3√3
- 2√3
- 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

3.5√3 cm

7√5 cm

7√3 cm

14 cm

**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 ∠PQR=130∘ , then the measure of ∠RPT is

50∘

30∘

45∘

40∘

**Q.**

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

Only if they are non-collinear.

Only if they are in the same plane.

Only if they are concentric.

- It is not possible.

**Q.**

How many circles can be drawn circumscribing a given triangle?

infinite

1

2

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?

ΔAXB≅ΔDXC by ASA postulate

ΔAXB≅ΔDXC by SAS postulate

∠BAX=∠CDX

AB=CD

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

- one
- two
- three
- 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:

- True
- False

**Q.**

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

Infinite

1

0

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

0

2

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_______

Sectors

Semicircles

Arcs

Tangents

**Q.**

How many circles can be drawn circumscribing a given triangle?

- 1

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

- True
- False

**Q.**

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

1

3

0

Data inadequate

**Q.**Draw a circle with centre C and radius 3.4 cm. Draw any chord ¯¯¯¯¯¯¯¯AB. Construct the perpendicular bisector of ¯¯¯¯¯¯¯¯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?

Yes, Yes

No, No

Yes, No

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?

Only if they are concentric.

- It is not possible.
Only if they are non-collinear.

Only if they are in the same plane.

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

- True
- False

**Q.**

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

- 2
- 3
0

- 1

**Q.**

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

Infinite

1

0

4

**Q.**

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

Yes, Yes

No, Yes

No, No

Yes, No