In `Delta ABC` with usual notation `r_1/(bc)+r_2/(ca)+r_3/(ab)` is

Statement I In a Delta ABC, if a lt b lt c and ri si inradius and r_(1), r_(2) ,r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

In DeltaABC, let b=6, c=10and r_(1) =r_(2)+r_(3)+r then find area of Delta ABC.

In any Delta ABC, prove the following : r_1=rcot(B/2)cot(C/2)

In Delta ABC , point M on AB and point N on AC are such that AM = (1)/(4)AC and AN =(1)/(4)AC . Prove that MN =(1)/(4) BC

Draw a Delta ABC with AB= 4 cm, BC = 9 cm and AC = 6 cm. Then construct a triangle similar to Delta ABC whose sides are 1 (1)/(2) times the corresponding sides of Delta ABC.

If a, b, c be the pth, qth and rth terms respectively of a HP, show that the points (bc, p), (ca, q) and (ab, r) are collinear.

If r and R are radii of the incircle and circum-circle of DeltaABC, then prove that : 8rR{cos ^(2) A//2 +cos ^(2) B//2 +cos ^(2) C//2} =2bc+2ca+2ab-a^(2) -b^(2) -c^(2).

In Delta ABC , P, Q and R are the midpoints of AB, BC and CA respectively. If PQ = 5 cm, QR = 8 cm and RP = 6.5 cm, find the perimeter of Delta ABC .

D, E, F are mid points of sides BC, CA, AB of Delta ABC . Find the ratio of areas of Delta DEF and Delta ABC .