Question

Chords AB and CD intersect each other in point M .P is center of circle . Radius of circle is 13cm and PM =5cm . Find product of CM into DM

Answer 1

Answer:

144

Step-by-step explanation:

Given Chords AB and CD intersect each other in point M .P is center of circle . Radius of circle is 13cm and PM =5cm . Find product of CM into DM

According to the theorem Inside a circle the product of their segments are equal when two chords intersect each other, The longest chord of a circle is diameter.

So draw a diameter in a circle passing through points P and M. The line AB is the diameter and P is the centre of circle.

 Since it is diameter , AB = 2 x radius

                                         = 2 x 13 = 26 cm

          MB = PY - PM = 13 - 5 = 8

         MA = PM + PA = 13 + 5 = 18

From the above theorem we have,

      CM x MD = MA x MB

       8 x 18 = 144

So CM x DM = 144 cm