Draw a circle of radius 4 cm- Draw two lines touching the circumference of the circle such that they intersect at an angle 60- Draw a quadrilateral joining the centre of circle- points at which lines are touching and at the point they intersect- -3 MARKS-

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Standard VI

Mathematics

Chord

Draw a circle...

Question

Draw a circle of radius 4 cm. Draw two lines touching the circumference of the circle such that they intersect at an angle 60⁰. Draw a quadrilateral joining the centre of circle, points at which lines are touching and at the point they intersect. [3 MARKS]

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Solution

Construction of circle: 1 Mark
Construction of intersecting lines: 1 Mark
Construction of quadrilateral: 1 Mark

Construction:

1) Draw a circle of radius 4 cm with centre O.

2) Take a point A on the circle. Join OA.

3) Draw a perpendicular to OA at A.

4) Draw a radius OB, making an angle of 120° (180° – 60°) with OA.

5) Draw a perpendicular to OB at point B. Let these perpendiculars intersect at P.

6) PA and PB are the required tangents inclined at angle of 60°

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$∠$ AOP = __ $^{\circ}$

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Draw a pair of tangents to a circle of any convenient radius, which are inclined to the line joining the centre of the circle and intersect at a point forming an angle of 45 degree with the line.

Q. The image of construction of two tangents inclined at

60^{\circ}

drawn to a circle of radius of 4cm is given below.

Arrange the steps of construction the in correct order.
1.Take a point A on the circumerence of the circle and join OA. Draw a perpendicular to OA at point A.
2.Draw radius OC, making an angle of

120^{\circ} (180^{\circ} - 60^{\circ})

.
3.Draw a circle of radius 4cm and mark its centre as O.
4.Draw a perpendicular to OC at point C.Let both the perpendiculars intersect at point P. PA and PC are the required tangents inclined at an angle of

60^{\circ}

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