Question

If ABC is a triangle, P is a point outside the triangle.

Then avecPA+bvecPB+cvecPC=(a+b+c)vecPK holds if K is?

• Circumcenter
• Centroid
• Any point
• None
• Incenter

Solution

We will modify this equation and elminate P so we get avecPA+bvecPB+cvecPC=(a+b+c)vecPK

avecA+bvecB+cvecC=(a+b+c)vecK

vecK = (avecA+bvecB+cvecC)/(a+b+c)

Here it is better if we remember that K is an incenter.

Though it is recommended to prove that K is an incenter.