Question

The relation between length of sides of triangle and segment's length from vertex to a point on opposite side. It is referred as:

• A. Pythagoras theorem
• B. Apollonius theorem
• C. Law of tangents
• D. None of the above

Answer 1

The correct option is B Apollonius theorem

Pythagoras theorem states relation between hypotenuse and oother two sides of a triangle.

Law of tangents states the relation between tangents of two angles of a triangle and the lengths of the opposing sides.

But, Apollonius' theorem states that given a triangle ABC, if D is any point on BC such that it divides BC in the ratio n:m (or $mBD=nDC$), then

$mA{B}^2+nA{C}^2=mB{D}^2+nD{C}^2+(m+n)A{D}^2$

Thus, it states the relation between length of sides of triangle and segment's length.

Hence, option C is correct.