MathDB

Find the Angle

Source: Indian RMO 2013 Paper 1 Problem 1

2/1/2014

Let

ABC

be an acute-angled triangle. The circle

\Gamma

with

BC

as diameter intersects

AB

and

AC

again at

P

and

Q

, respectively. Determine

\angle BAC

given that the orthocenter of triangle

APQ

lies on

\Gamma

.

geometrygeometry unsolved

Indian RMO- Paper 2

Source: Problem 1

12/11/2013

Prove that there do not exist natural numbers

x

and

y

with

x>1

such that ,

\frac{x^7-1}{x-1}=y^5+1

modular arithmeticnumber theory unsolvednumber theory

Indian RMO- Paper -3

Source:

12/11/2013

Find the number of eight-digit numbers the sum of whose digits is

4

Compositionsdigit sumElementary counting

Indian RMO - Paper -4[1]

Source:

12/12/2013

Let

\omega

be a circle with centre

O

. Let

\gamma

be another circle passing through

O

and intersecting

\omega

at points

A

and

B

.

A

diameter

CD

of

\omega

intersects

\gamma

at a point

P

different from

O

. Prove that

\angle APC= \angle BPD

geometry

Parallel Lines in a Circumcircle

Source: Indian RMO 2013 Mumbai Region Problem 1

2/1/2014

Let

ABC

be an isosceles triangle with

AB=AC

and let

\Gamma

denote its circumcircle. A point

D

is on arc

AB

of

\Gamma

not containing

C

. A point

E

is on arc

AC

of

\Gamma

not containing

B

. If

AD=CE

prove that

BE

is parallel to

AD

.

geometrycircumcircletrapezoidgeometry unsolved

1

Problems(5)