MathDB

4

Part of 2020 New Zealand MO

Problems(2)

p^2 - 6 and p^2 + 6 are both prime numbers

Source: New Zealand MO 2020 Round 1 p4

9/20/2021
Determine all prime numbers pp such that p2−6p^2 - 6 and p2+6p^2 + 6 are both prime numbers.
primesnumber theoryprime numbers
angle bisector wanted, internally tangent circles

Source: 2020 NZMO Round 2 p4

1/10/2021
Let Γ1\Gamma_1 and Γ2\Gamma_2 be circles internally tangent at point AA, with Γ1\Gamma_1 inside Γ2\Gamma_2. Let BCBC be a chord of Γ2\Gamma_2 which is tangent to Γ1\Gamma_1 at point DD. Prove that line ADAD is the angle bisector of ∠BAC\angle BAC.
geometryangle bisectortangent circles