Unizor - Geometry2D - Circles - Construction 9

Welcome to UNIZOR.COM http://www.unizor.com. 1. Construct a quadrangle, that can be inscribed into a circle (not given), by its given three sides and a diagonal. 2. Construct a rhombus by its side and a radius of an inscribed circle. 3. Circumscribe a right isosceles triangle around a given circle. 4. Construct an isosceles triangle by its base and a radius of an inscribed circle. 5. Construct a triangle by its side and two medians originating from the endpoints of this side. 6. Construct a triangle by three medians. 7. Given a circle and three points on it. Construct a triangle such that its three angle bisectors intersect a circle at given points. 8. Given a circle and three points on it. Construct a triangle such that its three altitudes intersect a circle at given points. Hint: prove that vertices of a triangle divide arcs between given points in halves. 9. Construct a triangle by three points of intersection of its median, altitude and angle bisector, originating from the same vertex, with its circumscribing circle. Hint: radius to a point of intersection of an angle bisector with a circle is parallel to an altitude.