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

Answer:

The value of product CM×DM=144

Step-by-step explanation:

Given Chords AB and CD of a circle intersect each other in point M. The center of the circle is P. The radius of the circle is 13 cm and PM=5 cm. We have to find the product CM×DM.

MF=PM+PF(radius)=5+13=18 cm

EM=PE-PM=13-5=8 cm

By intersecting chord theorem which states that when two chords intersect each other inside a circle, the products of their segments are equal.

CM×DM=EM×MF

⇒ CM×DM=8×18=144

hence, the value of product is 144.

Answer 2

Answer:

Step-by-step explanation:

MF=MP+PF

5+13=18

ME=PE-PM

13-5=8

Pm×me=cm×md

18×8=cm×md

144=cm×md

Refer to fig of above answer