Draw a line segment with length 7 cm. Now, draw arcs at one end with radius 3 cm and another end with radius 4 cm. The two arcs drawn will intersect at a point.

True

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False

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Solution

The correct option is A
True

For the arcs to intersect at any point not on the line segment, the sum of radii with which both the arcs are drawn must be greater than the length of the line segment.

So, if $r_{1} + r_{2} < A B$ , arcs won’t intersect at all.

If $r_{1} + r_{2} > A B$ , arcs will intersect.

If $r_{1} + r_{2} = A B$ , arcs will intersect on the line segment AB.

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Similar questions

Draw a line segment with length 7 cm now, draw arcs at one end with radius 3 cm and another end with radius 4 cm. The two arcs drawn will intersect at a point.

Draw a line segment with length 7 cm. Now, draw arcs at one end with radius 3 cm and another end with radius 4 cm. The two arcs drawn will intersect at a point.

Q. Steps for the construction of a parallelogram ABCD in which AB = 6 cm, BC = 4.5 cm and diagonal AC = 6.8 cm is given below.

Choose the correct order.

1. Draw AB = 6 cm.

2. With A as centre and radius 6.8 cm, draw an arc.

3. With A as centre and radius 4.5 cm, draw an arc.

4. With B as center and radius 4.5 cm draw another arc, cutting the previous arc at C. Join BC and AC.

5. With C as centre and radius 6 cm draw another arc, cutting the previously drawn arc at D. Join DA and DC.

Q. Choose the correct order for the construction of the rectangle ABCD with AB = 6 cm and BC = 4 cm.

1. Construct a perpendicular AE to AB at A such that AE is greater than 4 cm.
2. With D as centre and radius 6 cm, draw an arc.
3. With A as centre and radius 4 cm draw an arc so as to cut AE at D.
4. Draw a line segment AB = 6cm.
5. With B as centre and radius 4 cm, draw another arc so as to intersect previous arc at C.
6. Join DC and BC. Then ABCD is the required rectangle

Q. Steps for the construction of a quadrilateral ABCD with AB = 4 cm, BC = 6 cm, CD = 5.5 cm, AD= 5 cm and AC = 8 cm is given below.

Choose the correct order.

1. Draw a line segment AC of 8 cm.

2. With 4 cm as radius from A draw an arc.

3. With 5 cm as radius from A draw an arc to the opposite side of AC.

4. With 6 cm as radius cut the arc drawn in step 2. Let that point of intersection be B. Join AB and CB.

5. From C take 5.5 cm as radius and cut the arc drawn in step 4. Let the point of intersection be D. Join AD and CD.

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