What is the locus of points P for which perpendicular lengths (red=l, green=n, purple=m) to the sides of an isosceles triangle satisfy the condition red*green = purple²? mirangu.com/locus-pocus-ii/ By Marshall W. Buck

Two equilateral triangles sharing a vertex and several line segments. What’s the angle α? mirangu.com/shoulder-to-sh… Inspired by ナタデココ入り

Two regular pentagons, one of which has an extended side. What’s the angle α? mirangu.com/pentagon-offsp…

EHF is tangent to the purple circle at E, and EN is tangent to the red circle at N. A and C are the circle centers. A blue rectangle has three corners HEC and the point A on one side. Ratio of areas green square to orange quadrilateral? mirangu.com/bicyclic-trans… By Marshall W. Buck

Three circles and a line segment connecting three intersections. Prove that the three centres and the common intersection are concyclic. mirangu.com/the-fourth-cir…

Three equilateral triangles share a vertex. What is the area of the blue one in terms of green and red? mirangu.com/man-in-the-mid…

The incircle of ABC touches sides at I and J. D, E, F are the bases of altitudes from C, B, and A. The incenters of BDF of CEF are N and M, respectively. Show that JIMN is a parallelogram and that IM is perpendicular to BC. mirangu.com/the-fountain-p… By Marshall W. Buck

Is the blue area greater than, equal to, or less than the purple area? (Hint: the difference, if there is one, would be very small.) (Assume the horizontal lines are equidistant.) mirangu.com/balancing-rock/ By Marshall W. Buck

A quarter circle and a semicircle with several line segments, one of which is tangent to the semicircle. What is the area proportion semicircle : quarter circle? mirangu.com/the-helmet-vis… Inspired by SKG

A square with its centre and a right angle. What’s ad-bc? mirangu.com/centre-stage/ Inspired by Chris Wildhagen

The blue parallelogram’s vertex C lies on a green circle that intersects the diagonal BC at J. What is the length of the red segment? mirangu.com/circular-cuts/ By Marshall W. Buck

A regular pentagon and its circumcircle. What is blue : orange? mirangu.com/pentagon-pleas… Inspired by Chris Wildhagen

A square is divided in two regions. What fraction is grey? mirangu.com/ragged-mountai…

The blue unit circle has a diameter and several colored chords. The red chord bisects the angle between the green chords. Express the sum of the green chords in terms of the red and purple chords. mirangu.com/criss-cross-ch… By Marshall W. Buck

Two regular hexagons share a vertex. What is the angle α? mirangu.com/the-dutch-roll/

A regular hexagon is divided in four triangles and one quadrilateral. Express the hexagon area in terms of areas A, B and C. mirangu.com/tip-of-tipi/ Inspired by ナタデココ入り

The midpoint (center) of the incircle is I. R is the midpoint of the red segment and G is the midpoint of the green segment. Show the RIG makes a line. mirangu.com/middle-journey/ By Marshall W. Buck

We are going on a 1 month break. Starting September 23 you will find your daily dose of geometry again. For those of you who cannot live without, see mirangu.com/archives/ 😎