
Right triangle ABC, points D and E are in the side of BC. AD=AC
and BE=AB. How much is angle DAE?


In
,
and CD is of angle C.
Prove CA+DA=BC. 

Rectangle ABCD, P is in the side of BC and Q is in the side of
CD. PA intersects PQ in 45 degree. Prove BP+DQ=QP.


Circles O1 and O2, their chord AB=8, calculate the distance
between their centers (O1O2= ?). 

In
circle O,
AB and CD are diameters, chord EF is vertical for OC and goes
halves in OC. Prove
. 

A triangle ABC, side AB=a, the height on side AB is h.
Rectangle
EFGH is inscribed, see
image. How height is HE, the area of rectangle is maximum?
(Plot triangle ABC in setting AB=3 and its height = 3) 
