## Search found 73 matches

Tue Apr 17, 2018 10:17 am
Forum: Secondary Level
Topic: Easy Projective Geo
Replies: 3
Views: 3739

### Easy Projective Geo

Points \$A, B, C, D, E\$ lie on a circle and a point \$P\$ lie outside the circle. The given points such that (1) lines \$PB\$ and \$PD\$ are tangent to the circle, (2) \$P, A, C\$ are collinear and (3) \$DE\$ is parallel to \$AC\$.
Prove that: \$BE\$ bisects \$AC\$
Thu Apr 05, 2018 4:56 pm
Forum: Secondary Level
Topic: "Log"ing Problem!
Replies: 1
Views: 2415

### Re: "Log"ing Problem!

\$(24log_a2)=a^{128}+128\$ \$\Rightarrow log_a(log_a2^{24})=a^{128}+128\$ \$\Rightarrow log_a2^{24}=a^{a^{128}+128}\$ [According to the basis of logarithm] \$\Rightarrow 2^{24}=a^{a^{a^{128}+128}}\$ \$\Rightarrow a^{a^{128}.a^{a^{128}}}=2^{24}\$ \$\Rightarrow y^y=2^{24}\$ [Setting \$a^{a^{128}}=y\$] \$\Rightarrow...
Thu Apr 05, 2018 4:50 pm
Forum: Secondary Level
Topic: "Log"ing Problem!
Replies: 1
Views: 2415

### "Log"ing Problem!

Let \$a>1\$ and \$x>1\$ satisfy \$log_a(log_a(log_a2)+log_a24-128)=128\$ and \$log_a(log_ax)=256\$.
Find the remainder when \$x\$ is divided by \$1000\$
Mon Mar 12, 2018 10:30 am
Topic: BdMO National Secondary/Higher Secondary 2018/2
Replies: 1
Views: 772

### Re: BdMO National Higher Secondary 2018/2

Capture.PNG Let \$AC\$ and \$BD\$ meets at \$E\$. \$AD=a,BC=b\$ where, \$a<b\$. Easy to prove: \$\angle CAD=\angle ABE, \angle DBC=\angle BAE\$ We know, \$\angle BAD=\angle BAE+ \angle CAD=90^{\circ}\$ \$\Rightarrow \angle BAE+\angle ABE=90^{\circ}\$ Again, \$\angle ABE+\angle ADB=90^{\circ}\$ So, \$\angle BAE=\angle...
Sat Mar 10, 2018 12:13 am
Topic: BdMO National Secondary/Higher Secondary 2018/4
Replies: 2
Views: 919

### Re: BdMO National Higher Secondary 2018/4

\$21\$ I got.
Wed Mar 07, 2018 10:17 am
Topic: BdMO 2017 National Round Secondary 7
Replies: 13
Views: 3135

### Re: BdMO 2017 National Round Secondary 7

Told you before, if \$20\$ pictures can share more than two common color and not all of them share the same color, the answer is \$2\$.
[100% sure] Wed Mar 07, 2018 10:07 am
Topic: BDMO 2017 National round Secondary 5
Replies: 15
Views: 4046

### 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\$
Mon Mar 05, 2018 11:43 pm
Topic: BDMO 2017 National round Secondary 5
Replies: 15
Views: 4046

### Re: BDMO 2017 National round Secondary 5

Again a question. How can we say that \$A\$-centered circle will go through \$B\$?
Mon Mar 05, 2018 10:34 pm
Topic: BDMO 2017 National round Secondary 5
Replies: 15
Views: 4046

### Re: BDMO 2017 National round Secondary 5

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?
Mon Mar 05, 2018 8:50 pm