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 13cm and PM = 5cm .Find the product CM×DM .

Answer 1

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

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