problems #1

Geometry Level 3

The area of the circumcircle of A B C ABC where A B = 20 , B C = 21 , C A = 29 AB=20, BC=21, CA=29 is x π x \pi . Find x x .

This problem is part of the set Easy Problems


The answer is 210.25.

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3 solutions

Akash Deep
Nov 22, 2014

we find that the triangle is right angled. so the hypotenuse will become the diameter. therefore circumradius = 29/2 area of circle = pi * r^2. so x = r^2 x = 841/4 = 210.25

Highry Tan
Sep 13, 2014

ABC is a right triangle by the Pythagorean Theorem. Since that is the case, CA will be the diameter of the circumcircle of ABC, hence, the radius is \frac { 29 }{ 2 } , area is { \left( \frac { 29 }{ 2 } \right) }^{ 2 }\pi \quad units\quad =\quad \boxed { 210.25 } \pi \quad units.

Utkarsh Kumar
Sep 9, 2017

x π x\pi = π r 2 \pi \cdot r^2

Where r r is the circumradius.

So x x = r 2 r^2

And r r = a b c / 4 a r e a abc / 4area

By calculation x x = 210.25

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