17

Part of 2005 Sharygin Geometry Olympiad

Problems(1)

ruler construction, point such that a circle is tangent to the incircle

Source: Sharygin 2005 XI CR 17

A circle is inscribed in the triangle

ABC

and it's center

I

and the points of tangency

P, Q, R

BC

C A

AB

are marked, respectively. With a single ruler, build a point

K

at which the circle passing through the vertices B and

C

touches (internally) the inscribed circle.

geometryRulertangent circlesincircle