Question

Chord AB and CD of a circle intersect each other in point M. The centre of circle is P.The radius of a circle is 13cm and PM=5cm. Find the product CM×DM.

Answer 1

Answer:

CM x DM=144 cm.

Step-by-step explanation:

This question is related to intersecting chords theorem .Intersecting chords are two straight lines segments whose both end points lie on a circle and both are intersecting each other in a circle. The theorem states that:

When in a circle two chords intersect each other the product of their segment would be equal.

Now ,

OP = PQ =radius=13 cm.

OQ = diameter=13*2= 26 cm

AB=CD=chords

M=the point at which the chords intersect.

PM= 5 cm

0M = OP - PM= 13-5= 8 cm

QM=PM + PQ = 13+5=18 cm

Now according to the intersecting theorem we have:

CM x DM = OM X QM= 8*18 =144 cm

Answer 2

Answer CM x DM =144cm