Incircle of ` A B C` touches the sides BC, CA and AB at D, E and F, respectively. Let `r_1` be the radius of incircle of ` B D Fdot` Then prove that `r_1=1/2((s-b)sinB)/((1+sin(B/2)))`

Incircle of DeltaABC touches the sides BC, AC and AB at D, E and F, respectively. Then answer the following question angleDEF is equal to

Incircle of DeltaABC touches the sides BC, AC and AB at D, E and F, respectively. Then answer the following question The length of side EF is

Let the incircle with center I of A B C touch sides BC, CA and AB at D, E, F, respectively. Let a circle is drawn touching ID, IF and incircle of A B C having radius r_2dot similarly r_1a n dr_3 are defined. Prove that (r_1)/(r-r_1)dot(r_2)/(r-r_2)dot(r_3)/(r-r_3)=(a+b+c)/(8R)

The incircle of an isoceles triangle ABC, with AB=AC, touches the sides AB,BC and CA at D,E and F respecrively. Prove that E bisects BC.

In Figure, the incircle of A B C touches the sides B C ,\ C A and A B\ a t\ D ,\ E and F respectively. Show that A F+B D+C E=A E+B F+C D=1/2(P e r i m e t e r\ of\ A B C) .

Let the incircle of a Delta ABC touches sides BC, CA and AB at D,E and F, respectively. Let area of Delta ABC be Delta and thatof DEF be Delta' . If a, b and c are side of Detla ABC , then the value of abc(a+b+c)(Delta')/(Delta^(3)) is (a) 1 (b) 2 (c) 3 (d) 4

In DeltaABC , the incircle touches the sides BC, CA and AB, respectively, at D, E,and F. If the radius of the incircle is 4 units and BD, CE, and AF are consecutive integers, then

Let the incircle of DeltaABC touches the sides BC, CA, AB at A_(1), B_(1),C_(1) respectively. The incircle of DeltaA_(1)B_(1)C_(1) touches its sides of B_(1)C_(1), C_(1)A_(1) and A_(1)B_(1)" at " A_(2), B_(2), C_(2) respectively and so on. Q. In DeltaA_(4)B_(4)C_(4) , the value of angleA_(4) is:

Let the incircle of DeltaABC touches the sides BC, CA, AB at A_(1), B_(1),C_(1) respectively. The incircle of DeltaA_(1)B_(1)C_(1) touches its sides of B_(1)C_(1), C_(1)A_(1) and A_(1)B_(1)" at " A_(2), B_(2), C_(2) respectively and so on. Q. lim_(n to oo) angleA_(n)=

In an acute angled triangle A B C , a semicircle with radius r_a is constructed with its base on BC and tangent to the other two sides. r_b a n dr_c are defined similarly. If r is the radius of the incircle of triangle ABC then prove that 2/r=1/(r_a)+1/(r_b)+1/(r_c)dot