MathDB

There are given two intersecting lines

g_1,g_2

and a point

P

in their plane such that

\angle(g1,g2)\ne90^\circ

. Its symmetrical points on any point

M

in the same plane with respect to the given lines are

M_1

and

M_2

. Prove that:
(a) the locus of the point

M

for which the points

M_1,M_2

and

P

lie on a common line is a circle

k

passing through the intersection point of

g_1

and

g_2

. (b) the point

P

is an orthocenter of a triangle, inscribed in the circle

k

whose sides lie at the lines

g_1

and

g_2

Problem 3