Question

AB and CD are two chords of a circle which intersect at a point O inside the circle. It is given that, AB = 10 cm, CO= 1.5 cm and DO = 12.5 cm. What is the ratio between the larger and smaller among AO and BO?

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