Online Geometry Problems

Geometry Problem 82. Area of the Contact Triangle, Inradius, Circumradius. High School, College, Math Education

Given a triangle ABC of area S, the incircle of center I, the inradius r, and the circumradius R. If S1 is the area of the contact triangle DEF, prove that: .
 


 

See also:
Original problem 82 art
Kaleidoscope problem 82
Sketch problem art 82
 
 

HINTS:


See: Problem 81.


CONTACT TRIANGLE:

The contact triangle of a triangle ABC (figure above), also called the intouch triangle, is the triangle DEF formed by the points of tangency of the incircle of triangle ABC with triangle ABC.

 


AREA OF A TRIANGLE:

Semiperimeter and Inradius Formula

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | Art | 81-90 | Circle Tangent Line | Email | View or post a solution | by Antonio Gutierrez