MathDB

Given two planes

\pi _1,\ \pi _2

intersecting orthogonally in space. Let

A,B

be two distinct points on the line of intersection of

\pi _1

and

\pi _2,

and

C

be the point which is on

\pi _2

but not on

\pi_1.

Denote by

P

the intersection point of the bisector of

\angle {BCA}

and

AB

, and denote

S

by the circumference on

\pi _1

with a diameter

AB.

For an arbiterary plane

\pi _3

which contains

CP,

D,E

are the intersection points of

\pi_3

and

S,

then prove that

CP

is the bisector of

\angle {DCE}.

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