geometry that will make you mad!

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Zahin Hasin Rudro
Posts:11
Joined:Sun Jul 12, 2015 3:52 am
geometry that will make you mad!

Unread post by Zahin Hasin Rudro » Fri Jul 17, 2015 3:12 pm

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?

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Raiyan Jamil
Posts:138
Joined:Fri Mar 29, 2013 3:49 pm

Re: geometry that will make you mad!

Unread post by Raiyan Jamil » Sun Nov 29, 2015 10:06 am

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.
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Zahin Hasin Rudro
Posts:11
Joined:Sun Jul 12, 2015 3:52 am

Re: geometry that will make you mad!

Unread post by Zahin Hasin Rudro » Mon Dec 07, 2015 12:39 pm

thank you very much.

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