Question

The circumcentre of triangle DEF is O and DM is perpendicular to EF,DE= 5cm,DF=3.5cm,DM=2cm. What is the radius of the nine point circle of the triangle?

Answer 1

The radius of the nine point circle of triangle DEF is 1cm.

Step-by-step explanation:

To find the radius of the nine point circle of triangle DEF, we need to use the following formula:

r = √[(R2-2Rr)/(4R)]

Where R is the circumradius and r is the inradius of the triangle. In this case, the circumradius is OM = DM = 2cm.

Substituting the values into the formula, we get:

r = √[(22-2*2*r)/(4*2)]

After simplifying, we find that r = 1cm. The radius of the nine point circle of triangle DEF is 1cm.