2097

Prove the red point is fixed.

2096

Prove the red angles are congruent.

2095

The green point is the midpoint of a side of the yellow triangle. Prove the red and green points are concyclic.

2094

The blue shape is a parallelogram. Prove the red lines are perpendicular.

2093

The blue angles are complementary. Prove the red lines are perpendicular.

2092

Prove the red and yellow points are concyclic.

2091

The green points trisect a side of the yellow triangle. The blue shape is a parallelogram. Prove the red line segments are congruent.

2090

The blue shape is an isosceles trapezoid. Prove the red circles are tangent to each other.

2089

The blue shapes are isosceles trapezoids. Prove the red line segments are congruent.

2088

The yellow points are the midpoints of sides of the yellow triangle. Prove the red line segments are congruent.

2087

Prove the red line bisects the red angle.

2086

Prove the red angles are congruent.

2085

The circles are congruent. Prove the sum of the red arcs equals the circumference of a circle.

2084

Prove $ab = rR$.

2083

The yellow shape is a trapezoid. Prove the red points are collinear.

2082

The green lines are parallel to sides of the blue equilateral triangle. Prove the red triangle is equilateral.

2081

Prove $m = \frac{1}{2}\lvert a-b+c-d\rvert$.

2080

Prove the red lines are concurrent.

2079

The yellow triangle is isosceles. Prove the red line segment is the sum of blue line segments.

2078

Prove the external angle bisectors of a parallelogram form a rectangle the sum of whose diagonals equals the perimeter of the parallelogram.

2077

Prove the red lines are parallel.

2076

The green point inside the blue triangle is reflected about the midpoint of each side of the triangle. Prove the red and blue triangles are congruent.

2075

Given a grid of squares. Prove the red and blue angles are congruent.

2074

Find the measure of the red angle.

2073

Prove $a:b = 9:8$.

2072

Prove $A = r^2$.

2071

The blue and yellow circles are congruent. Prove the red points are concyclic.

2070

Prove $a^2+b^2 = c^2$.

2069

Prove the red line bisects the blue arc.

2068

Prove the red lines are concurrent.

2067

The green rectangle and circle are concentric. Prove the red line is parallel to sides of the rectangle.

2066

Prove, in the yellow triangle, a median, an altitude, and an angle bisector are concurrent.

2065

The red tangent lines are parallel to the sides of the triangle. Prove opposite sides of the yellow hexagon are congruent.

2064

The triangle has sides $a$, $b$, and $c$. Prove the red line segments are congruent with length $\frac{1}{2}(a+b-c)$.

2063

Prove the red and blue points are collinear.

2062

The blue triangle is equilateral. Prove the red lines are perpendicular.

2061

Prove the red lines are perpendicular.

2060

The yellow shape is a square. Prove the red points are collinear.

2059

Prove the red line is tangent to the blue circle.

2058

Prove the red line segments are congruent.

2057

Prove the red lines are perpendicular.

2056

The blue and yellow triangles are equilateral. Prove the sum of the red angles is $120^\circ$.

2055

The blue point is the orthocenter of the blue triangle. Prove the red and blue points are collinear.

2054

Prove the red line segment is double the blue line segment.

2053

Prove the red lines are perpendicular.

2052

The red line is the perpendicular bisector of the green line segment. Prove the red line is tangent to the blue circle.

2051

Prove the blue line segment is the radius of the red circle.

2050

Prove the red line segments are congruent.

2049

Prove the red line segments are congruent and the blue line segments are congruent.

2048

Prove the blue and red areas are the same.

2047

Prove the red line segment is the radius of the blue circle.

2046

The base of the blue triangle is the arithmetic mean of the other two sides. The blue point is the centroid of the blue triangle. The green point is the orthocenter of the green triangle. Prove the red, blue, and green points are collinear.

2045

Prove the red points are concyclic.

2044

Prove the red lines are concurrent.

2043

Prove the red points are collinear.

2042

The blue triangle is isosceles. Prove the red lines are perpendicular.

2041

The blue and green trapezoids share a base. Prove the red points are collinear.

2040

The blue and green trapezoids share a base. Prove the red points are collinear.

2039

The green triangle is a rotation of the blue triangle. Prove the red triangle is similar to both of them.

2038

The blue line is the perpendicular bisector of a side of the red triangle. The semiperimeter of the green triangle is $s$. Prove the area of the red triangle is $ds$.

2037

Prove the red line bisects the red angle.