Question

Chords AB and CD intersect at point M. According to the diagram, which pair of numbers could represent lengths of segments CM and DM ?
A) 2 and 7
B) 2 and 10
C) 2.5 and 6.5
D) 3 and 6

Answer 1

Answer:

Step-by-step explanation:

Since the product of the intersecting chords should be equal

==> AM x BM = CM x DM

==> 4 x 5 = CM x DM

==> 20 = CM x DM

Therefore CM x DM = 2 X 10

Answer 2

Answer:

Step-by-step explanation:

When two chords intersect each other inside a circle, the products of their segments are equal.

In this figure, AB and DM are two chord intersect at point M. AB chord is cut into two line segments AM and BM. The CD chord is cut into two line segments CM and DM.

As per the theorem.

$AB\times BM=CM\times DM\\\\\Rightarrow 4\times5=CM\times DM\\\\\Rightarrow 20=CM\times DM$

Now find the factor of 20.

Therefore, Factor of 20 are =1,2,4,5,10 and 20

$CM\times DM=2\times10=20$

Therefore, the option B is correct.