Vedant
Last Activity: 7 Years ago
We take ,
CD = BC/a, AE = AC/b, BF/c where a,b and c are ratios
Then BD = BC – CD = BC – BC/a = BC(a – 1)/a
CE = AC – AE = AC – AC/b = AC(b – 1)/b
AF = AB – BF = AB – AB/c = AB(c – 1)/c
Therefore,
BD * CE * AF = [AB * BC * AC * (a – 1) * (b – 1) * (c – 1)] / abc ...1
and CD * AE * BF = k * [AB * BC * AC] / abc ...2
On compairing 1 and 2, we find that k = (a – 1) * (b – 1) * (c – 1)
where a = BC / CD, b = AC / AE and c = AB / BF
