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Theorem 4: Triangle and Parallelogram

O is any poin...

Question

O is any point in triangle ABC P,Q,R and S are the points on OA,OB,BC and AC.such that PQRS is the parallelogram and PQllAB.prove that QRllOC

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. O is any point in the interior of a triangle ABC. Prove that

1. AB + AC > OB + OC

2.AB + BC + CA > OA + OB + OC

3.OA + OB + OC > 1/2(AB + AC + BC)

Q. If any point

O

in the interior of a triangle ABC. Prove that AB

+

+

>

+

+

O

is any interior point of triangle

A B C

O A + O B + O C > 1 / 2 (A B + B C + A C)

Q. If O is a point in space, ABC is a triangle and D, E, F are the mid-points of the sides BC, CA and AB respectively of the triangle, prove that

\vec{O A} + \vec{O B} + \vec{O C} = \vec{O D} + \vec{O E} + \vec{O F}

Q. If O is any point in the interior of a triangle ABC, then

O A + O B + O C > \frac{1}{2} (A B + B C + C A)

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Theorem 4: Triangle and Parallelogram

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