Question

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

Answer 1

Answer:

CM * DM = 126

Step-by-step explanation:

Given :

The chords AB and CD intersect at M.

Center of the circle is P.

Radius of the circle = 13 cm

PM = 5 cm

To find :

CM * DM

Solution:

Intersecting chords theorem states that when two chords intersect each other inside a circle, the product of their segments are equal.

Also, diameter is the largest chord of the circle.

Now, draw a diameter of the circle passing through points P and M. It is the line XY as shown in the attachment.

Length XY = 2 * radius = 2 * 13 =26 cm

MY = PY - PM = 13 - 5 =7 cm

XM = XP + PM = 13 + 5 = 18 cm

By the intersecting chords theorem we have,

CM * DM = XM * YM =18 * 7 =  126

∴ CM * DM = 126

Answer 2

above and is right

but,from step

MY=PY- PM= 13- 5=8

MX=PX+PM=13+5=18

By chord intersecting theorem

CM×MD=MX×MY

8×18=144

CM×DM=144