## BDMO 2017 National round Secondary 5

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
Absur Khan Siam
Posts: 65
Joined: Tue Dec 08, 2015 4:25 pm
Location: Bashaboo , Dhaka

### Re: BDMO 2017 National round Secondary 5

Tasnood wrote:
Mon Mar 05, 2018 10:34 pm
Sorry for Interrupt. My answer was same of #Nahin but this solution is new to me.
How can we find the radius of two circles same?
\$AC = AB\$ , radius of the \$\widehat{BC}\$
\$BC = AB\$ , radius of the \$\widehat{AB}\$

Thus, \$AC = BC\$
"(To Ptolemy I) There is no 'royal road' to geometry." - Euclid

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BDMO 2017 National round Secondary 5

Durjoy Sarkar wrote:
Mon Mar 05, 2018 10:06 pm
radius of two big circle are same. let X be the point where little circle is tangent.
it is well known the center of little circle, tangent point are lies on \$OB\$.
\$MO=OX\$
\$BX= BO+OX=BO+MO \$
The placement of point \$X\$ is not clear to me.I didn't understand the \$2\$nd line of it.

Tasnood
Posts: 73
Joined: Tue Jan 06, 2015 1:46 pm

### Re: BDMO 2017 National round Secondary 5

Again a question. How can we say that \$A\$-centered circle will go through \$B\$?

ahmedittihad
Posts: 181
Joined: Mon Mar 28, 2016 6:21 pm

### Re: BDMO 2017 National round Secondary 5

Both have \$AB\$ as radius.....
Frankly, my dear, I don't give a damn.

Tasnood
Posts: 73
Joined: Tue Jan 06, 2015 1:46 pm

### Re: BDMO 2017 National round Secondary 5

Durjoy Sarkar wrote:
Mon Mar 05, 2018 10:06 pm
radius of two big circle are same. let X be the point where little circle is tangent.
it is well known the center of little circle, tangent point are lies on \$OB\$.
\$MO=OX\$
\$BX= BO+OX=BO+MO \$
You proved \$BX=OB+OM\$, not \$AB=OB+OM\$

Rangon Roy Utsab
Posts: 6
Joined: Wed Aug 03, 2016 11:01 pm
Location: Rangpur, Bangladesh.

### Re: BDMO 2017 National round Secondary 5

Tasnood wrote:
Wed Mar 07, 2018 10:07 am
Durjoy Sarkar wrote:
Mon Mar 05, 2018 10:06 pm
radius of two big circle are same. let X be the point where little circle is tangent.
it is well known the center of little circle, tangent point are lies on \$OB\$.
\$MO=OX\$
\$BX= BO+OX=BO+MO \$
You proved \$BX=OB+OM\$, not \$AB=OB+OM\$
Look carefully and you will notice that \$BX\$ and \$AB\$ are radii of the same circle centered \$B\$