and circumcenter 
.
,
the midpoints of 
,
.
with diameter 
,
at a point 
.
meets line 
at 
.
and 
intersect at a point 
on 
.
Prove that: 
is the sum of 
square numbers
Let 
and 
is the sum of 
is the sum of 
Y by Adventure10, Mango247
A line through the vertex 
of an isosceles triangle 
(
) cuts its base 
at 
so that the radius of the incircle of triangle ABD equals that of the excircle of triangle 
externally touching side 
(and the extensions ol 
and 
- see figure). Prove that this radius is 
the height 
of the triangle dropped from a base vertex.
(I. Sharygin)
of an isosceles triangle 
(
) cuts its base 
at 
so that the radius of the incircle of triangle ABD equals that of the excircle of triangle 
externally touching side 
(and the extensions ol 
and 
- see figure). Prove that this radius is 
the height 
of the triangle dropped from a base vertex.
(I. Sharygin)
This post has been edited 1 time. Last edited by parmenides51, Aug 21, 2019, 1:08 AM
