In an acute triangle ABC, BH, CQ and AR are altitudes, the angle "A" is equal to 50°, find the measure of the angle QRH.

Question

anonymous · Answer

I've tried to draw it, this is what i get.

hero · Answer

From what book are you studying?

anonymous · Answer

Many differents, this problem was given by a teacher based on one similar from one Pogorelov´s book.
I dont have the solutionary.

hero · Answer

Name of Pogorelov's book?

anonymous · Answer

The name is just "Geometry"

hero · Answer

Yes, but it's probably not in English

ganeshie8 · Answer

u familiar wid cyclic quadrilaterals

anonymous · Answer

Yes, and i think that the QBCH is cyclic.

ganeshie8 · Answer

thats true, but that quadrilateral wont help us. we need to take useful cyclic quadrilaterals

ganeshie8 · Answer

in which two vertices wud be A and R

ganeshie8 · Answer

lets take  the cyclic quadrilateral AQRC

$\angle CRQ + 50 = 180 $

ganeshie8 · Answer

can u think of another cyclic quadrilateral we can use

anonymous · Answer

Ok, the ABRH is cyclic.
 So  <BRH +50 = 180.

ganeshie8 · Answer

perfect ! rest is easy

anonymous · Answer

Oh, 
Then <CRH=<BRQ= 130-x
And

130-x + 130-x +x = 180
260 - x=180
x = 80 !!

Thanks.

ganeshie8 · Answer

np.. good work !