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The ratio between the circumference and diameter of any circle is _______

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#### Solution

The ratio between the circumference and diameter of any circle is **π**

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#### RELATED QUESTIONS

A chord of a circle of radius 10 em subtends a right angle at its centre. The length of the chord (in em) is

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`(B) 10 sqrt2`

`(C)5/sqrt2`

`(D) 10sqrt 3`

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Choose correct alternative answer and fill in the blank.

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The circle which passes through all the vertices of a triangle is called ______.

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find the radius of the circle.

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( ii ) ΔBPC ≅ ΔBQA

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**Use the figure given below to fill in the blank:**

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**Use the figure given below to fill in the blank:**

Tangent to a circle is _______.

**Use the figure given below to fill in the blank:**

________ is a radius of the circle.

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(ii) Assign a special name to AB.

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(i) Draw radii PA and PB such that ∠APB = 45°.

(ii) Shade the major sector of the circle

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**Draw circle with the radii given below.**

2 cm

**Draw circle with the radii given below.**

3 cm

**Draw a circle with the radii given below.**

4 cm

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Diagram |
Points in the interior of the circle |
Points in the exterior of the circle |
Points on the circle |

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A line segment which joins any two points on a circle is a ___________

The longest chord of a circle is __________

The radius of a circle of diameter 24 cm is _______

A part of circumference of a circle is called as _______

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radius (r) |
diameter (d) |
Circumference (C) |

15 cm |

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radius (r) |
diameter (d) |
Circumference (C) |

1760 cm |

Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).

radius (r) |
diameter (d) |
Circumference (C) |

24 m |

All the radii of a circle are _______________

The ______________ is the longest chord of a circle

A line segment joining any point on the circle to its center is called the _____________ of the circle

A line segment with its end points on the circle is called a ______________

Twice the radius is ________________

Find the diameter of the circle

Radius = 10 cm

Find the diameter of the circle

Radius = 6 cm

Find the radius of the circle

Diameter = 24 cm

Find the radius of the circle

Diameter = 30 cm

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Diameter = 76 cm

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A, B, C are any points on the circle with centre O. If m(arc BC) = 110° and m(arc AB) = 125°, find measure arc AC.

In figure, chords AC and DE intersect at B. If ∠ABE = 108°, m(arc AE) = 95°, find m(arc DC).

In the figure, segment PQ is the diameter of the circle with center O. The tangent to the tangent circle drawn from point C on it, intersects the tangents drawn from points P and Q at points A and B respectively, prove that ∠AOB = 90°

**Given:** A circle inscribed in a right angled ΔABC. If ∠ACB = 90° and the radius of the circle is r.

**To prove:** 2r = a + b – c

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In the figure, O is the centre of the circle, and ∠AOB = 90°, ∠ABC = 30°. Then find ∠CAB.

In the figure, a circle touches all the sides of quadrilateral ABCD from the inside. The center of the circle is O. If AD⊥ DC and BC = 38, QB = 27, DC = 25, then find the radius of the circle.

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In the figure, O is the centre of a circle, AB is a chord, and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to ______

If d_{1}, d_{2} (d_{2} > d_{1}) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle, then ______

If a number of circles pass through the endpoints P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.

If an isosceles triangle ABC, in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, find the area of the triangle.

If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is ______.

In figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ______.

In figure, ∠AOB = 90º and ∠ABC = 30º, then ∠CAO is equal to ______.

In figure, if AOB is a diameter and ∠ADC = 120°, then ∠CAB = 30°.

If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.

Two chords AB and AC of a circle subtends angles equal to 90º and 150º, respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.

In figure, O is the centre of the circle, BD = OD and CD ⊥ AB. Find ∠CAB.

Draw two acute angles and one obtuse angle without using a protractor. Estimate the measures of the angles. Measure them with the help of a protractor and see how much accurate is your estimate

In the given figure, O is the centre of the circle. Name all chords of the circle.

In the given figure, O is the centre of the circle. Name a chord, which is not the diameter of the circle.

In the given figure, O is the centre of the circle. Shade the smaller segment of the circle formed by CP.

From the figure, identify the centre of the circle.

From the figure, identify a diameter.

From the figure, identify two points in the interior.

From the figure, identify a point in the exterior.

Draw any circle and mark

- it's centre
- a radius
- a diameter
- a sector
- a segment
- a point in its interior
- a point in its exterior
- an arc

Say true or false:

The centre of a circle is always in its interior.

A figure is in the form of rectangle PQRS having a semi-circle on side QR as shown in the figure. Determine the area of the plot.

A circle of radius 3 cm with centre O and a point L outside the circle is drawn, such that OL = 7 cm. From the point L, construct a pair of tangents to the circle. Justify LM and LN are the two tangents.

If radius of a circle is 5 cm, then find the length of longest chord of a circle.

AB is a chord of a circle with centre O. AOC is diameter of circle, AT is a tangent at A.

Write answers to the following questions:

- Draw the figure using the given information.
- Find the measures of ∠CAT and ∠ABC with reasons.
- Whether ∠CAT and ∠ABC are congruent? Justify your answer.

The circumcentre of a triangle is the point which is ______.