Construction of a Circle with Known Radius

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Question 3

Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained if the diameters are perpendicular to each other? How do you check your answer?

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Question 2

With the same centre O, draw two circles of radii 4 cm and 2.5 cm

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Question 5

Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether $\overline{AB}$ and $\overline{CD}$ are at right angles.

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On a circle of radius 3 cm draw its two chords. Then construct the perpendicular bisector of these chords.
Where do they meet? [4 MARKS]

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Question 51

State whether the statements are true or false:

With a given centre and a given radius, only one circle can be drawn.

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Draw a circle with center O and radius 6 cm. Draw two non-intersecting circles with radii 3 cm each and centers as P and Q respectively passing through O. Now, join P and Q. Draw the diameter of the bigger circle RS such that it is perpendicular to PQ. Join PQRS. PQRS is a:

1. Rhombus

2. Rectangle

3. Square

4. Trapezium

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Draw a circle with centre C and radius 3.4 cm. Draw any chord. Construct the perpendicular bisector of and examine if it passes through C.

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Draw a circle with centre O using compass and ruler. Make smaller circles such that they are:
i) non-intersecting
ii) passing through the point O
iii) touching the circumference of the bigger circle. [3 MARKS]

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Question 4

Draw any circle and mark points A, B, and C such that:
a) A is on the circle.

b) B is in the interior of the circle.

c) C is in the exterior of the circle

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Find the perimeter of the semicircular region.

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Draw a line segment of length 12.8 cm. Using compasses; divide it into four equal parts. Verify by actual measurement.

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With of length 6.1 cm as diameter draw a circle.

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Draw a circle. Now draw any of its two diameters and mark them AC and BD. Join the points A, B, C and D. If ABCD is a square, the diameters must be ___ to each other.

Q. Construct a quadrilateral, ABCD has AB = 3.0 cm, BC = 4.0 cm, CD = 5.0 cm, DA = 3.5 cm and diagonal AC = 4.5 cm [2 MARKS]

Q. Suppose you are given a circle. Give the construction to find its centre.

1. Both options B & C.
2. The center lies on the bisector of the angle betwee any two chords of the circle
3. The center lies on the perpendicular bisectors of any two chords of the circle
4. The center lies on the mid point of any chord of the circle

Q. Three equal circles of radius 1 cm touches each other. What is smallest radius of circle touching all three.

Q. Draw a circle of radius $3$cm.At a point $P$ on it, draw a tangent to the circle without using centre.

Q. Draw a circle and name its centre, a radius, a diameter and arc.

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Draw a circle with center O and radius $6cm$. Draw two non-intersecting circles with radii $3cm$ each and centers as P and Q respectively passing through O. Now, join P and Q. Draw the diameter of the bigger circle RS such that it is perpendicular to PQ. Join PQRS.
PQRS is a:

1. Rhombus

2. Trapezium

3. Rectangle

4. Square

Q. Draw the figure according to the given information and answer the questions.

1. $3\sqrt{2}$
2. $2\sqrt{3}$
3. $3\sqrt{3}$
4. None of these

Q. Draw a circle of radius $5$ cm. In the circle, draw a chord $AB=6$ cm, then shade the minor and major segments.

Q. Draw a circle $4.5cm$ radius & divide the circle in $8$ equal parts.

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Draw a circle with center O with radius 5 cm. Draw any one of the diameters. With same center A, draw another circle with radius 3 cm. Draw any one of the diameters for this circle too. If you join the ends of both the diameters, the figure you will get is:

1. Parallelogram

2. Rectangle

3. Square

4. Trapezium

Q. Perimeter of a circle is $10\pi$. Find the radius of the circle and then draw the circle.

Q. After the circumcenter is constructed, one can complete the circumscribed circle with the radius length equal to:

1. the smallest side length of the triangle.
2. the distance from the intersection to any one side of the triangle.
3. the distance from the intersection to a vertex.
4. None of these

Q. Draw a circle and mark-
(a) its centre (b) a radius (c) a segment (d) its largest chord (e) a sector (f) an arc

Q. Draw a circle with centre $O$ and radius $2.5cm$. Draw two radii $OA$ and $OB$ such that $\angle AOB={60}^{\circ }$. Measure the length of chord $AB$.

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Draw a circle and mark a point X on the exterior of the circle and point Y in the interior of the circle. [1 MARK]

Q. Draw any circle and mark a point in its exterior.

Q. The diameter of a circle is $14cm$, find the radius.