Question

Given: Circumscribed △ELT, EL=14,
LT=17, ET=15.
Find: EI, LJ, and ST

Answer 1

Answer:

EI = 6; LJ = 8; ST = 9

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Given,

In $\Delta ELT$ $EL=14, LT=17, ET=15.$

$EI$ and $ES$ are two tangents from external point E

Therefore, $EI=ES=x$

$LI$ and $LJ$ are two tangents from external point L

Therefore, $LI=LJ=y$

$TS$ and $TJ$ are two tangents from external point T

Therefore, $TS=TJ=z$

We know that,

$EL=14\\\\\Rightarrow EI+LI=14\\\\\Rightarrow x+y=14\\\\\Rightarrow x=14-y\text{..............equation-1}$

$LT=14\\\\\Rightarrow LJ+TJ=17\\\\\Rightarrow y+z=17\\\\\Rightarrow z=17-y\text{..............equation-2}$

$ET=14\\\\\Rightarrow ES+TS=15\\\\\Rightarrow x+z=15\\\\\Rightarrow 14-y+17-y=15\text{ [putting the value of x and y we get]}\\\\\Rightarrow 31-2y=15\\\\\Rightarrow 31-15=2y\\\\\Rightarrow 16=2y\\\\\Rightarrow y=8$

putting the value of y in equation-1 we get,

$x=14-y\\\\x=14-8\\\\x=6$

putting the value of y in equation-2 we get,

$y=17-z\\\\z=17-y\\\\z=17-8\\\\z=9$

therefore the value of EI=6, LJ=8 and ST=9