Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4774. (February 2016)

B. 4774. The parabolas $\displaystyle p_1$ $\displaystyle \big(y=-x^2+b_1 x+c_1\big)$ and $\displaystyle p_2$ $\displaystyle \big(y=-x^2+b_2 x+c_2\big)$ are tangent to the parabola $\displaystyle p_3$ $\displaystyle \big(y=x^2+b_3x+c_3\big)$. Prove that the line connecting the points of tangency is parallel to the common tangent of $\displaystyle p_1$ and $\displaystyle p_2$.

Kvant

(5 pont)

Deadline expired on March 10, 2016.

### Statistics:

 65 students sent a solution. 5 points: 54 students. 4 points: 3 students. 3 points: 3 students. 1 point: 4 students. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, February 2016