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

3 cm

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#### Solution

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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:**

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

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Construct a triangle ABC with AB = 5 cm, ∠B = 60° and BC = 6. 4 cm. Draw the incircle of the triangle ABC.

Construct a triangle PQR in which, PQ = QR = RP = 5.7 cm. Draw the incircle of the triangle and measure its radius.

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

2 cm

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

4 cm

Draw a circle of any radius. Show one diameter, one radius, and one chord on that circle.

In the table below, write the names of the points in the interior and exterior of the circle and those on the circle.

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

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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) |

15 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) |

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 _______________

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Find the diameter of the circle

Radius = 10 cm

Find the diameter of the circle

Radius = 8 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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In the adjoining figure, seg DE is the chord of the circle with center C. seg CF⊥ seg DE and DE = 16 cm, then find the length of DF?

If O is the center of the circle in the figure alongside, then complete the table from the given information.

The type of arc

Type of circular arc |
Name of circular arc |
Measure of circular arc |

Minor arc | ||

Major arc |

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

In figure, O is the centre of a circle, chord PQ ≅ chord RS. If ∠POR = 70° and (arc RS) = 80°, find

(i) m(arc PR)

(ii) m(arc QS)

(iii) m(arc QSR)

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In the adjoining figure, Δ ABC is circumscribing a circle. Then, the length of BC is ______

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In the adjoining figure ‘O’ is the center of the circle, ∠CAO = 25**° **and ∠CBO = 35**°**.** **What is the value of ∠AOB?

If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then OP = `asqrt(3)`

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In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Prove that the tangent to the circle at P bisects BC.

In figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to ______.

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.

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.

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.

From the figure, identify a sector.

Is every chord of a circle also a diameter?

Say true or false:

Two diameters of a circle will necessarily intersect.

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.

A 7 m broad pathway goes around a circular park with a circumference of 352 m. Find the area of road.

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.