## National BDMO 2016 : Junior 8

### National BDMO 2016 : Junior 8

In $\bigtriangleup ABC$ , $\angle A = 20$, $\angle B = 80$, $\angle C = 80$, $BC = 12$ units. Perpendicular $BP$ is drawn on $AC$ from from $B$ which intersects $AC$ at the point $P$. $Q$ is a point on $AB$ in such a way that $QB = 6$ units. Find the value of $\angle CPQ$.

The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.

- Charles Caleb Colton

- Charles Caleb Colton

- ahmedittihad
**Posts:**147**Joined:**Mon Mar 28, 2016 6:21 pm

### Re: National BDMO 2016 : Junior 8

This was a nice problem. Let $C'$ be the reflection of $C$ w.r.t $BP$. Now, $\angle C'BC = 2*10$. So, $\angle QBC'=80-20=60$. As $QB=6, BC'=12$ and $\angle QBC' =60$ we see that $\triangle QBC'$ is a $30-60-90$ triangle. So, $\angle BQC'=90$. We get, $BQC'P$ is cyclic. So, $\angle CPQ= \angle BPC+\angle BPQ=\angle BPC+BC'Q=90+30=120$.

Q.E.D

Q.E.D

Frankly, my dear, I don't give a damn.

- Kazi_Zareer
**Posts:**86**Joined:**Thu Aug 20, 2015 7:11 pm**Location:**Malibagh,Dhaka-1217

### Re: National BDMO 2016 : Junior 8

Solution:

We cannot solve our problems with the same thinking we used when we create them.

- Thamim Zahin
**Posts:**98**Joined:**Wed Aug 03, 2016 5:42 pm

### Re: National BDMO 2016 : Junior 8

I had made the reflection but didn't get that it was a right triangle. Have to draw diagram as scale from now on.

I think we judge talent wrong. What do we see as talent? I think I have made the same mistake myself. We judge talent by the trophies on their showcases, the flamboyance the supremacy. We don't see things like determination, courage, discipline, temperament.