Question

M is the incenter of triangle ABC. Find the lengths of MD and DC. (Look at pic)

Answer 1

Part 1)
`MD=9\ units`

Part 2)
`DC=12\ units`

Explanation:

Step 1

Find the length of MD

we know that

The incenter is the intersection of the angle bisectors of the three vertices of the triangle. Is the point forming the origin of a circle inscribed inside the triangle

so

In this problem

`MD=ME=MF` ------> is the radius of a circle inscribed inside the triangle

we have that

`MF=9\ units`

therefore

`ME=9\ units`

`MD=9\ units`

Step 2

Find the length of DC

we know that

In the right triangle MDC

Applying the Pythagoras theorem

`MC^(2) =MD^(2)+DC^(2)`

we have

`MD=9\ units`

`MC=15\ units`

substitute

`15^(2) =9^(2)+DC^(2)`

`DC^(2)=225-81`

`DC=√(144)\ units`

`DC=12\ units`