Circle
Tangents The
Problems : A
Let
ABCD be a convex quadrilateral (no
reflex angles), and suppose the quadrilateral has an inscribed circle, that is,
a circle inside the shape that touches all four of the linesegments AB,
BC, CD,
DA .
Prove
that AB + CD = BC + DA.
Deduce
that if a parallelogram has an inscribed circle, then it is a rhombus. B
(Harder)
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