M CUBE: MatheMatics by Maheshwari – Page 4 – Enjoy the WORLD of MATHEMATICS

Enjoy the WORLD of MATHEMATICS

September 2, 2019 M CUBE: Math-e-Matics by Maheshwari RADIUS OF INCIRCLE

Derivation of Formula for Radius of Incircle

The radius of in-circle is given by the formula DERIVATION

September 1, 2019 M CUBE: Math-e-Matics by Maheshwari RADIUS OF CIRCUMCIRCLE

Derivation of Formula for Radius of Circumcircle

The formula for the radius of the circle circumscribed about a triangle (circumcircle) is given by

September 1, 2019 M CUBE: Math-e-Matics by Maheshwari AREA OF CYCLIC QUADRILATERAL

Derivation of Formula for Area of Cyclic Quadrilateral

For a cyclic quadrilateral with given sides a, b, c, and d, the formula for the area is given by DERIVATION OF THE FORMULA

August 30, 2019August 30, 2019 M CUBE: Math-e-Matics by Maheshwari CRMO

A polynomial is called a Fermat polynomial if it can be written as the sum of the squares of two polynomials with integer coefficients. Suppose that f(x) is a Fermat polynomial such that f(0) = 1000. Prove that f(x) + 2x is not a Fermat polynomial

CRMO 2013

August 30, 2019 M CUBE: Math-e-Matics by Maheshwari CRMO

Find all 4-tuples (a, b, c, d) of natural numbers with a ≤ b ≤ c and a! + b! + c! = 3^d

CRMO 2013

August 30, 2019 M CUBE: Math-e-Matics by Maheshwari CRMO

Find the number of eight-digit numbers the sum of whose digits is 4.

CRMO 2013

August 30, 2019 M CUBE: Math-e-Matics by Maheshwari CRMO

Suppose that m and n are integers such that both the quadratic equations x^2 + mx − n = 0 and x^2 − mx + n = 0 have integer roots. Prove that n is divisible by 6.

CRMO 2013

August 30, 2019August 30, 2019 M CUBE: Math-e-Matics by Maheshwari CRMO, Olympiads

Let ABC be a triangle with ∠A = 90◦ and AB = AC. Let D and E be points on the segment BC such that BD : DE : EC = 3 : 5 : 4. Prove that ∠DAE = 45◦ .

CRMO 2013

August 30, 2019August 30, 2019 M CUBE: Math-e-Matics by Maheshwari CRMO

Find all primes p and q such that p divides q^2 − 4 and q divides p^2 − 1.

CRMO 2013

August 30, 2019August 30, 2019 M CUBE: Math-e-Matics by Maheshwari CRMO

Let ABC be an acute angled triangle. The circle Γ with BC as diameter intersects AB and AC again at P and Q, respectively. Determine ∠BAC given that the ortho-center of triangle AP Q lies on Γ

CRMO 2013

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