`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 ,Ea n dF` respectively. Show that `A D x B E x C F=D B x E C x F A`

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 a parallelogram A B C D , the bisectors of /_A\ a n d\ /_B meet at Odot Find /_A O Bdot

let P an interioer point of a triangle A B C and A P ,B P ,C P meets the sides B C ,C A ,A B in D ,E ,F , respectively, Show that (A P)/(P D)=(A F)/(F B)+(A E)/(E C)dot

let P an interioer point of a triangle A B C and A P ,B P ,C P meets the sides B C ,C A ,A B in D ,E ,F , respectively, Show that (A P)/(P D)=(A F)/(F B)+(A E)/(E C)dot

From a point O inside a triangle A B C , perpendiculars O D ,O Ea n dOf are drawn to rthe sides B C ,C Aa n dA B , respecrtively. Prove that the perpendiculars from A ,B ,a n dC to the sides E F ,F Da n dD E are concurrent.

In a A B C , D and E are points on the sides A B and A C respectively such that D E// B C If A D=4 , A E=8 , D B=x-4 , and E C=3x-19 , find x .

X Y is a line parallel to side B C of /_\ A B C . B E || AC and C F || A B meet X Y in E and F respectively. Show that a r( A B E)=a r( A C F) .

In Figure, find x . Further find /_B O C ,\ /_C O D\ a n d\ /_A O D .

In a A B C ,D and E are points on sides A B a n d A C respectively such that B D=C E . If /_B=/_C , show that DE || BC .

A triangle A B C is inscribed in a circle with centre at O , The lines A O ,B Oa n dC O meet the opposite sides at D , E ,a n dF , respectively. Prove that 1/(A D)+1/(B E)+1/(C F)=(acosA+bcosB+ccosC)/