,
,
be the feet of the perpendiculars from 
to the lines 
,
,
,
if and only if the bisectors of 
and 
are concurrent with 
.
be reals such that 
. Prove that
.
be the feet of the altitudes from 
to 
to 
and 
as the reflections of 
be the circumcircle of 
.
with 
with 
is the circumcenter of 
can be inscribed within a circle.
where 
are lengths of parallel sides and 
are other two sides.
Y by
(a) Let the incenter of 
be 
. We connect other 
vertices and divide into small triangles which has area 
and 
. Find the area of the inscribed circle of .
(b) Let
be a parallelogram. Point 
is on 
respectively. If ![$[AED]=7,[EBF]=3,[CDF]=6$](//latex.artofproblemsolving.com/5/2/1/5216270fbb581387c483d9ff939ae335d0d5f92e.png)
, then find ![$[DEF].$](//latex.artofproblemsolving.com/6/0/7/6075a04047406821a1eea62e6310b518a18e1279.png)
(Here ![$[XYZ]$](//latex.artofproblemsolving.com/c/7/6/c7608a3e97e44fc5bcf0cd62a1f7dfc0a0a2e7d4.png)
denotes the area of 
)
be 
. We connect other 
vertices and divide into small triangles which has area 
and 
. Find the area of the inscribed circle of .(b) Let
be a parallelogram. Point 
is on 
respectively. If ![$[AED]=7,[EBF]=3,[CDF]=6$](http://latex.artofproblemsolving.com/5/2/1/5216270fbb581387c483d9ff939ae335d0d5f92e.png)
, then find ![$[DEF].$](http://latex.artofproblemsolving.com/6/0/7/6075a04047406821a1eea62e6310b518a18e1279.png)
(Here ![$[XYZ]$](http://latex.artofproblemsolving.com/c/7/6/c7608a3e97e44fc5bcf0cd62a1f7dfc0a0a2e7d4.png)
denotes the area of 
)This post has been edited 2 times. Last edited by hsiangshen, Nov 21, 2020, 2:43 PM
(
