On a line segment with length 7 cm, draw an arc at one end with radius 3 cm and another arc at the other 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.

If, $r_{1} + r_{2} < A B$
$\Rightarrow$ Arcs won’t intersect at all.

If $r_{1} + r_{2} > A B$
$\Rightarrow$ Arcs will intersect.

If $r_{1} + r_{2} = A B$
$\Rightarrow$ Arcs will intersect on the line segment AB.

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