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In triangle ABC,

 

Any help would be appreciated!

 Jul 29, 2020
 #1
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For some reason, the text didn't save. 

 

In triangle ABC,  

 Jul 29, 2020
 #2
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Really confused right now, 

In triangle ABC, angle B = 90 degrees. Semicircles are constructed on sides AB, AC and BC as shown. Show that the total area of the shaded region is equal to the area of triangle ABC.

 Jul 29, 2020
 #3
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Let the sides be a, b and sqrt (a^2+b^2)

 

So the radii are       \(\frac{a}{2},\quad \frac{b}{2},\quad \frac{\sqrt{a^2+b^2}}{2}\)

 

Area of triangle =  ab/2

 

Area of big semicircle = \(0.5 \pi*\frac{(a^2+b^2)}{4}=\frac{(a^2+b^2)\pi}{8}\)

 

Sum of little white segments = \(\frac{(a^2+b^2)\pi}{8}-\frac{ab}{2}=\frac{(a^2+b^2)\pi-4ab}{8}\)

 

Sum of the 2 smaller semicircle =       \(0.5*\pi((\frac{a}{2})^2+(\frac{b}{2})^2)= \pi(\frac{a^2+b^2}{8})\\ \)

 

 

You can finish it

 Jul 29, 2020

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