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Incentrics

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December 22, 2019

geometryeuclidean geometry

Problem Statement

a) In a

XYZ

triangle, the incircle tangents the

XY

and

XZ

sides at the

T

and

W

points, respectively. Prove that:

XT = XW = \frac {XY + XZ-YZ} {2}

Let

ABC

be a triangle and

D

is the foot of the relative height next to

A.

Are

I

and

J

the incentives from triangle

ABD

and

ACD

, respectively. The circles of

ABD

and

ACD

tangency

AD

at points

M

and

N

, respectively. Let

P

be the tangency point of the

BC

circle with the

AB

side. The center circle

A

and radius

AP

intersect the height

D

at

K.

b) Show that the triangles

IMK

and

KNJ

are congruent c) Show that the

IDJK

quad is inscritibed

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