ABC is a right angle triangle where angle A is right angle. The perpendicular
drawn from A on BC intersects BC at point D. A point P is chosen on the circle
drawn through the vertices of ΔADC such that CP perpendicular to BC and AP = AD. If a
square is drawn on the side BP, the area is 340 square units. What is the area of
triangle ABC?
geometry that will make you mad!
- Raiyan Jamil
- Posts:138
- Joined:Fri Mar 29, 2013 3:49 pm
Re: geometry that will make you mad!
In the quadrilateral APCD, you'll see that all angles are 90 degrees having a pair of equal adjacent sides; AP=AD. therefore it's a square i.e AD=AP=CP=CD. Now, as the square is inscribed in a circle, then the centre of the circle will be on the point of intersection of the diagonals AC and PD. So, in triangle ABC, angle ACB is 45 degrees. Therefore, BD=CD=CP. Let BD be 'a'. Therefore according to the pythagoras theorem, $(2a)^2+a^2=BP=340$ i.e. $5a^2=340$ or, $a^2=68$.Now, you'll see that it's the area of APCD, whose area is equal to that of ABC. So, the area of ABC is 68 sq. units.
A smile is the best way to get through a tough situation, even if it's a fake smile.
-
- Posts:11
- Joined:Sun Jul 12, 2015 3:52 am
Re: geometry that will make you mad!
thank you very much.