Mathematical and Physical Journal
for High Schools
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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