Home Geometry Problems Art All Problems 351-360 Semicircle Circular Segment Area of a Triangle View or post a solution 
Problem 360. Area of a triangle, Curvilinear triangles, Circles, Diameters.
Level: High School, College, SAT Prep.

In the figure below, ABC is an acute triangle with area S. Circles of diameters AB, BC, and AC form three curvilinear triangles of areas S1, S2, and S3, respectively, and one internal curvilinear triangle of area S4.
Prove that 2S = S1 + S2 + S3 - S4.

Area of triangle, circle, curvilinear
 
 
 

 

See Also:

 

Classical Theorems

 

Right triangle, Incircle, Angle

Proposed Problem 361.
Right triangle, Incircle, Incenter, Tangency points, Angle.

 

Cyclic quadrilateral, Rhombus

Proposed Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus.

 

Isosceles triangle 80 80 20

Proposed Problem 358.
Isosceles triangle 80-80-20, Circle, Angles, Congruence.

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