Unizor - Geometry2D - Circles - Construction 6
Channel: Zor Shekhtman on UNIZOR Education
Date: 2012-01-12

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1. Given a circle and a sector in it bordered by two radiuses and an arc. Inscribe a circle into this sector tangential to both radiuses and an arc.
2. Inscribe three circles of equal radiuses into a given circle such that each circle is tangential to all others.
3. Given a circle and a point inside it. Construct a chord containing this point such that the difference between two segments a given point divides a chord is equal to a given segment.
Hint: Draw a concentric circle through a given point.
4. Given two intersecting circles. Construct a secant that contains one of intersection points between these circles such that its part inside a union of two given circles is congruent to a given segment.
Note: Reduce to constructing a triangle by two sides and a median between them.
5. Given a straight line, a point on it and a point outside it. Construct a circle tangential to a given line at a given point and containing the other given point.
6. Inscribe a circle of a given radius into given angle.
7. Inscribe a circle into a given angle if a distance between the vertex of an angle and a circle is given.
8. Construct a circle tangential to two given circles with a given point of tangency on one of them. Consider cases when
(a) one of given circles is outside another and constructed circle should be outside of both of them,
(b) one of given circles is outside another and constructed circle should be outside of one, but should contain another given circle,
(c) one of given circles is outside another and constructed circle should contain both given circles.