Problem 3

Let

ABC

be an equilateral triangle. Let

P

be a point on

AC

and

Q

a point on

AB

so that triangles

ABP

and

ACQ

are acute. Let

R

and

S

be the orthocentres of triangles

ABP

and

ACQ

, respectively. Let

T

be the common point of the segments

BP

and

CQ

. Find all possible values of

\angle CBP

and

\angle BCQ

such that triangle

TRS

is equilateral.

Step 1 of 8: Name the two angles

\alpha=\angle CBP,\qquad\beta=\angle BCQ.

Detailed analysis

Use alpha and beta for the two angles whose possible values are requested.