Mirangu
@Mirangu1
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Your daily dose of vitamin G. A geometry puzzle a day keeps the doctor away.
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Joined October 2020
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A square contains a triangle. What fraction of the square is red?
32
46
198
Three triangles are glued together. The green ones are based on a common line. What’s the angle α?
25
27
161
A square contains a yellow right triangle with an area of 11. What is the square’s area?
22
29
119
Three congruent squares share three vertices. What’s the angle α?
24
14
114
A square containing an isosceles triangle with given side lengths. What fraction is red?
13
20
111
Three congruent squares inscribed in a rectangle. What fraction of the total area is green?
16
19
108
A quarter circle with two chords of given length. What is the area of the orange quadrilateral?
26
16
110
Three tangent semicircles and a circle. One tangency point is shown. Prove that red : green = yellow : blue. Inspired by
@Ahmet____CETiN
12
17
105
A rectangle is divided into four similar triangles. What fraction is blue?
17
19
106
Two intersecting circles and a common tangent. The two tangency points are shown in black. Prove that the three red points are collinear. Inspired by Di Pasquale ea.
7
20
103
A square and a rectangle share two vertices. If the square has twice the area of the rectangle, what’s the angle α?
19
19
100
Three squares are placed in a row. Prove that the red vertices are collinear.
15
22
99
Two equilateral triangles share a vertex. What is the proportion red : green? Inspired by
@Cshearer41
15
19
96
Two squares of which three vertices form an isosceles triangle. What is the angle α?
25
19
96
A square containing two overlapping equilateral triangles. What’s the length proportion a : b?
15
20
93
Two perpendicular squares inside a circle. The circle centre is located on the side of one square. The line segment connecting two vertices has length a. What is the circle area?
18
25
94
Four semicircles and three line segments. What’s the proportion yellow : orange? Inspired by Posamentier.
18
24
92
Three squares and a circle. The areas of the squares are given. What is the area of the circle?
19
20
92
An equilateral triangle containing a right triangle and a line segment. What fraction is pink?
17
15
86
A square containing a rectangle and a tangent quarter circle. What fraction is orange?
18
14
87
A square and an equilateral triangle inside a right triangle. Prove that the three red vertices are collinear.
19
18
87
Three squares, one of which has a side length of 2. What is the green area?
27
12
87
A green quadrilateral of which two sides are tangent to a quarter circle of radius r. What is its area?
14
16
85
A rectangle containing a right triangle. What’s red : blue? Inspired by Posamentier.
26
12
85
Two rectangles share a vertex. Two line segments connecting opposing vertices and the common side intersect in a single point. Prove that the rectangles are similar.
13
15
84
Two squares, three circles and a common tangent. What fraction is coloured? Inspired by
@panlepan
and
@edsouthall
17
22
87
A square and an overlapping isosceles triangle. What is the angle α? Inspired by
16
14
85
Two quarter circles and a red circle tangent to two chords. What fraction is red?
11
17
83
An equilateral triangle with given distances between its vertices and an exterior point. What’s its side length x? Inspired by Posamentier.
19
23
85
Two congruent circles and a triangle. Prove that the triangle is isosceles.
13
19
83
Two tangent circles and a third circle touching the line segment connecting their centres in the tangency point. Prove that the red points (centre and two intersection points) are collinear.
16
13
84
A rectangle is divided in six similar triangles. What is the proportion green : yellow : red : blue?
14
15
83
A circle containing an equilateral triangle and three squares. What fraction is purple?
10
15
85
Two circles with three common tangents. Three tangency points are shown. Prove that they are collinear.
10
15
85
A circle containing a regular pentagon and two equilateral triangles. All shown points are on the circle. What’s the angle α?
14
21
81
A semicircle with two inscribed circles tangent to an altitude. What’s the angle α?
16
17
85
A rectangle containing a circle and a line segment connecting the top side to the bottom tangency point. What is its area in terms of lengths a and b?
8
16
82
A square containing a semicircle, a tangent and a line segment from the tangency point. What fraction is green?
13
12
80
Three squares and two perpendicular line segments. What is red : yellow : blue?
15
10
82
Two equilateral triangles share a side midpoint. What is the angle α?
8
12
82
A square containing four smaller squares. What fraction of its area is orange? Inspired by
@archimedes_000
18
14
77
A semicircle and an inscribed circle. Prove that the circle centre is on the parabola. Inspired by
@MatthewArcus
15
12
78
A triangle containing an altitude and the inscribed circle. One tangency point is shown. The red line segments have equal length. What is the proportion of the triangle sides a : b : c?
11
16
79
Two circles, two radii and three chords. What is the length of radius x in terms of a, b and c? Inspired by Posamentier.
11
16
76
A regular hexagon, a square with its diagonals, an equilateral triangle and a circle. Prove that the hexagon and the circle are concentric.
10
10
78
A triangle containing two congruent squares. Each square has 1/3 the perimeter and 1/6 the area of the triangle. What’s the triangle side length proportion a : b : c?
10
13
78
A regular hexagon shares a vertex with an equilateral triangle of area 7. What is the area of the hexagon? Inspired by
@NATA_de_Koko1
17
19
78
A unit square and a point on the inscribed circle. What is a²+b²+c²+d²? Inspired by
@preshtalwalkar
14
16
79
Four squares, three of which are coloured. What’s the area of the blue one? Inspired by
@sonukg4india
14
16
76
An equilateral triangle and three line segments. What’s the angle α?
19
17
74
A semicircle, a square and a chord. If the square has area 32, what is the semicircle area?
17
9
75
Two squares inside a circle. What is the circle area in terms of length a?
15
15
77
Three squares, two of which share a vertex. What is the total area?
15
10
76
A square containing a red square of variable size sharing a vertex with a blue rectangle. What is the maximal blue fraction?
6
6
72
A square containing a semicircle, a circle and two tangents. What’s the angle α? Inspired by
@Ahmet____CETiN
20
15
76
A circle, a semicircle, a chord and an altitude. What is the length of the latter in terms of a and b? Inspired by Posamentier
18
17
73
Three semicircles and a circle all touching each other. The diameters of the two smallest semicircles are given. The large triangle connects three tangency points. What is the area of the green quadrilateral? Inspired by
@JuanPV_78
13
17
73
Three semicircles and a circle. Three centres are shown in green. What’s the proportion red : blue?
17
12
74
Two circles and two common tangents. Prove that the blue triangle is isosceles.
11
21
73
A square and an equilateral triangle. An extended side and diagonal meet in a point. What is the angle α? Inspired by
18
14
71
A square, a circle and its centre. Prove that the six red points are on one circle.
13
14
73
Three tangent semicircles and two coloured triangles. What’s the proportion yellow : green?
13
14
72
A square divided by three line segments. The red and blue areas are equal. What’s the length proportion a : b?
6
16
73
Two squares and a slanted rectangle share three vertices. What is the total area? Inspired by
@gs_bangalore
15
13
70
A circle tangent to a triangle side and to the two other extended sides. What is its diameter? Inspired by
@preshtalwalkar
15
14
71
A square with several line segments. Prove that the blue ones are parallel. Inspired by
@Ahmet____CETiN
14
14
70
An orange square and a blue rectangle with two congruent inscribed circles. What is the angle α? Inspired by
@EylemGercek
17
12
70
A regular pentagon and a circle through two of its vertices and its centre. What’s the angle α? Inspired by
@gs_bangalore
14
15
70
A regular pentagon with a diagonal and a right triangle. What’s the angle α?
12
13
72
Two circles inscribed an a trapezium divided by a perpendicular line segment. What is the proportion of its length a and the side b?
15
13
72
A regular hexagon and a square share a vertex. What is the area proportion square : hexagon?
15
16
70
Three squares are placed as shown. What fraction of the total area is green?
11
14
70
A square with an extended side inside another square. What fraction of the latter is blue? Inspired by
@gs_bangalore
17
19
71
Two congruent squares inscribed in a rectangle with given side lengths. What is the total orange area?
23
17
70
Two semicircles, a tangent and an altitude to the tangency point. Prove that the red triangle is isosceles.
19
11
68
A semicircle and a circle are tangent. The tangency point is shown. Prove that the two coloured triangles are similar.
10
14
69
Two regular pentagons are placed side by side. What’s the proportion blue : green?
11
14
68