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Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2016 India PRMO
4
4
Part of
2016 India PRMO
Problems
(1)
2016 preRMO p4, <C=90^o, AD = DE = EF = FB, CD^2 +CE^2 +CF^2 = 350
Source:
8/9/2019
Consider a right-angled triangle
A
B
C
ABC
A
BC
with
∠
C
=
9
0
o
\angle C = 90^o
∠
C
=
9
0
o
. Suppose that the hypotenuse
A
B
AB
A
B
is divided into four equal parts by the points
D
,
E
,
F
D,E,F
D
,
E
,
F
, such that
A
D
=
D
E
=
E
F
=
F
B
AD = DE = EF = FB
A
D
=
D
E
=
EF
=
FB
. If
C
D
2
+
C
E
2
+
C
F
2
=
350
CD^2 +CE^2 +CF^2 = 350
C
D
2
+
C
E
2
+
C
F
2
=
350
, find the length of
A
B
AB
A
B
.
geometry
right triangle