`O` is a point in the exterior of ` A B Cdot` what symbol ` > , <\ or\ =` will you use to complete the statement `O A+O BddotA B ?` write two other similar statements and show that `O A+O B+O C >1/2(A B+B C+C A)`

In figure, O is a point in the interior of a triangle ABC, O D_|_B C ,O E_|_A C and O F_|_A B . Show that (i) O A^2+O B^2+O C^2-O D^2-O E^2-O F^2=A F^2+B D^2+C E^2 (ii) A F^2+B D^2+C E^2=A W^2+C D^2+B F^2

A B C D IS A PARALLELOGRAM AND O is any point in its interior. Prove that: a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(^(gm)A B C D) Given: A parallelogram A B C D\ a n d\ O is a point in its interior. To Prove: a r\ (\ A O B)+\ a r( C O D)=a r\ ( B O C)+a r( A O D)

Let C be the mid-point of an arc A B of a circle such that m\ hat A B=183^0dot If the region bounded by the arc A C B and line segment A B is denoted by S , then the centre O of the circle lies in the interior of S (b) in the exterior of S on the segment A B (d) on A B and bisects A B

In figure A B=A C\ a n d\ C P||B A and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A (ii) A B C P is a parallelogram

In Figure, A B C is an isosceles triangle in which A B=A CdotC P A B and A P is the bisector of exterior /_C A D of A B C . Prove that /_P A C=/_B C A and (ii) A B C P is a parallelogram.

O is any point on the diagonal B D of the parallelogram A B C Ddot Prove that a r( O A B)=a r( O B C)

In Fig.,which of the following statements are true: Point B is the interior of /_AOB Point B is the interior of /_AOC Point A is the interior B of /_AOD point C is the exterior of /_AOB Point D is the exterior of /_AOC.

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ \ E G B)=1/6a r\ (A B C D)

D is the mid-point of side B C of A B C and E is the mid-point of B Ddot If O is the mid-point of A E , prove that a r( B O E)=1/8a r( A B C)