MathDB

In the Cartesian plane, let

G_1

and

G_2

be the graphs of the quadratic functions

f_1(x) = p_1x^2 + q_1x + r_1

and

f_2(x) = p_2x^2 + q_2x + r_2

, where

p_1 > 0 > p_2

. The graphs

G_1

and

G_2

cross at distinct points

A

and

B

. The four tangents to

G_1

and

G_2

A

and

B

form a convex quadrilateral which has an inscribed circle. Prove that the graphs

G_1

and

G_2

have the same axis of symmetry.

Problem Statement