A triangle with sides a, b, c, when extended to whiskers of opposite side length, forms the “Conway Circle”. What is the area of the circle in terms of the expressions a+b+c, ab+bc+ca, abc of the side lengths a, b, c.
A blue flagpole is erected near a drilling site. Lines are drilled perpendicular to the flagpole guy wires and meet at the bottom of the orange drilling pipe. What is the ratio of distances green to red?
Tangents to the blue circle (ABC) intersect at a point K, and the line AK intersects (ABC) at H. D is the midpoint of BC. Show that the green circle (DHB) is tangent to the line AB.
A cathedral is erected on two hills, the side circular arcs whose centers are the hill ends, and so that the right (and left) side arcs are orthogonal. Show that the tip of the spire is directly above where the hills meet.
Tangent lines QC and EC meet at C. A point D on QC has DC=1 and QD=2. The line ED intersects the circle at G, and the line HGI is parallel to QDC. What is HG/GI?
What is the area of a green quadrilateral that fits inside a quarter circle, and has perpendicular diagonals?
If X is the midpoint of the segment connecting the centers of the upper and lower arcs, and JK is perpendicular to XH, then show that H is the midpoint of JK.
A is the center of a unit circle. What is the distance AG if the distance AC = x?
Two tangent circles and a third circle between the centers. Show that the 3 circles have a common tangent line, and that the middle point of tangency is directly above the point where blue and green touch.
Green and blue “turkeys” with feet fixed at points A, B, C, D along the line, have their feathers interleaved. Show that every green-blue pair of circles intersect in points that are collinear with a single fixed point on the ground.