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Circle O is centered at the point of origin with point P = (3 , 4) lying on it. The red line l : 3x + 4y - 7 = 0 intersects the circle at points A and B, as shown.  What is the area of quadrilateral AOBP?

 

 Jul 28, 2020
 #1
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The circle is x^2+y^2 = 25, so system of equations with 3x+4y-7 = 0. We get (-3, 4) and (117/25, -44/25). Four coords are (0, 0), (-3, 4), (3, 4), (4.68, -1.76). Use Shoelace Theorem (more info https://artofproblemsolving.com/wiki/index.php/Shoelace_Theorem)

 

Using the Shoelace theorem, we get the area as 21.5.

 

You are very welcome!

:P

 Jul 28, 2020

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