ADGEOM 1205 * ADGEOM 1212 * ADGEOM 1213 * ADGEOM 1214

#1205

 

Dear friends,

 

T_aT_bT_c is the extouch triangle of ABC.

Erect perpendicular segments A'T_a, B'T_b, C'T_c on the extouch points such that

A'T_a = B'T_b = C'T_c = radius of incircle of ABC. (See image attached)

Then, AA', BB', CC' concur. 

 

Is this known?

 

Regards,

Emmanuel.

emmanuel antonio josgarca

 

#1212

 

Dear friends,

 

Let A" be the reflection of A' wrt T_a. Define B'', C''  cyclically.

The incenter is on the circle define by A'', B'', C'' .

 

Best regards,

Emmanuel.

 

#1213

Dear Emmanuel,
A''  is the reflection of I in the perpendicular bisector of BC. Therefore, OA'' = OI. Similarly, OB'' = OC'' = OI.
A'', B'', C'',  and I are on a circle, center O.
Best regards
Sincerely
Paul Yiu

#1214

Dear Paul Yiu,

 

Thank you very much.

 

Best regards,

Emmanuel.