MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 2
11
11
Part of
2020 LIMIT Category 2
Problems
(1)
Point inside Isosceles right triangle
Source: LIMIT 2020 Cat 2 Obj P11
5/25/2020
△
P
Q
R
\triangle PQR
△
PQR
is isosceles and right angled at
R
R
R
. Point
A
A
A
is inside
△
P
Q
R
\triangle PQR
△
PQR
, such that
P
A
=
11
,
Q
A
=
7
PA=11, QA=7
P
A
=
11
,
Q
A
=
7
, and
R
A
=
6
RA=6
R
A
=
6
. Legs
P
R
‾
\overline{PR}
PR
and
Q
R
‾
\overline{QR}
QR
have length
s
=
a
+
b
2
s=\sqrt{a+b\sqrt{2}}
s
=
a
+
b
2
, where
a
a
a
and
b
b
b
are positive integers. What is
a
+
b
a+b
a
+
b
?
limit
geometry