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

O is any point in the interior of A B Cdot Prove that A B+A C > O B+O C A B+B C+C A > O A+O B+O C O A+O B+O C >1/2(A B+B C+C A)

In Figure, A B=A C ,\ D is the point in the interior of A B C such that " "/_D B C=" "/_D C Bdot Prove that A D bisects B A C\ of A B Cdot

From a point O in the interior of a A B C , perpendiculars O D ,\ O E and O F are drawn to the sides B C ,\ C A and A B respectively. Prove that: (i) A F^2+B D^2+C E^2=O A^2+O B^2+O C^2-O D^2-O E^2-O F^2 (ii) A F^2+B D^2+C E^2=A E^2+C D^2+B F^2

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 E^2+C D^2+B F^2

In Fig., which of the following statements are true: (i) Point B is the interior of /_A O B (ii) Point B is the interior of /_A O C (iii)Point A is the interior of /_A O D (iv)point C is the exterior of /_A O B (v)Point D is the exterior of /_A O Cdot

A B C D is a parallelogram and O is any point in its interior. Prove that: (i) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(A B C D) (ii) 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 (a) 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 C is an isosceles triangle in which A B=A Cdot and C 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 inside a triangle A B C . The bisector of /_A O B ,/_B O C and /_C O A meet the sides A B ,B C and C A in point D ,E and F respectively. Show that A D * B E * C F=D B * E C * F A

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 (i) /_P A C=/_B C A (ii) A B C P is a parallelogram