an easy exercise in geometry ..

wats the answer ??

not now .. give yours then i will confirm. .

no no

E is the midpoint of arc BAEC !

and EOC is a right angle just that ..

l1 + l2 ??

good Q enjoyed solving it

yes celestine it is l1+l2 ..

the TITLE says its an EASY exercise

but i derived ans in 4-5 steps

is there a 1 step elegant sol ??
ill post my method tomorrow

just applying basic properties thats all .. the number of lines doesnt matter

ok i thought there was some special property used that i dint know

yes i think my derivation is simpler .. have a look

let BD=DC =a

let BE =d

in ABD cos(180-α)=l₁²+AB²-BD²/(2l₁AB

we have ABcosα as AE=l2 and AB²=AE²+BE²

so we get -2l1l2=l1²+l2²+BE²-BC² (BD=BC) but BC²-BE²=x² which we require

thus we get x²=l1²+l2²+2l1l2