2224

Prove the red line segments are congruent.

2223

The blue circles are congruent. Prove the red quadrilateral is tangential.

2222

Prove the red circle bisects the blue line segment.

2221

Prove the red points are collinear.

2220

Prove the red points are concyclic.

2219

Prove the red and yellow points are concyclic.

2218

2217

Find the measure of the red angle.

2216

Prove the red angles are congruent.

2215

Prove the red angles are congruent.

2214

Prove the red circle is tangent to the yellow incircle.

2213

Prove the red line bisects the blue angle.

2212

The blue points are the midpoints of the green chords. Prove the red lines are concurrent.

2211

Prove the red lines are perpendicular.

2210

Prove the red angles are congruent.

2209

The yellow shape is a square. Prove the red angles are congruent.

2208

Find the measure of the red angle.

2207

The blue angle is double the green angle. The red angle is triple the green angle. Prove the red line segment is the sum of the blue line segments.

2206

Prove the blue trapezoid is tangential.

2205

Prove the red line bisects the blue line segment.

2204

The yellow triangles are isosceles whose vertex angles sum to $360^\circ$. Prove each red angle is half of the blue angle sharing its vertex.

2203

The circles are congruent. Prove $a^2+b^2=c^2$.

2202

Prove $R=\sqrt{AP\cdot AQ}$.

2201

Prove the red point is the incenter of the triangle.

2200

Prove the red vector is $\frac{2}{3}$ the sum of the blue vectors.

2199

Prove the sum of red line segments is $$\sqrt{\frac{1}{2}\left(a^2+b^2+c^2\right) + 2A\sqrt{3}}$$ where $A$ is the area of yellow triangle.

2198

Prove the red line is parallel to sides of the blue parallelogram.

2197

The red lines trisect the sides of the yellow quadrilateral. Prove the red line segments trisect each other.

2196

Prove $c=\frac{1}{2}(a+b)$.

2195

Prove the red medians trisect the blue line segment.

2194

Prove the red points are concyclic.

2193

Prove the red line segments are congruent.

2192

Prove the radius of the red circle equals the semiperimeter of the right triangle.

2191

The blue lines are parallel to the sides of the triangle. Prove $ABC=8DEF$.

2190

Prove the red angles are congruent.

2189

Prove $c=\frac{b}{a}(a+b)$.

2188

Find the measures of the red angles.

2187

Prove the red angles are congruent.

2186

Prove the red line is tangent to the green circle.

2185

Prove the red and purple points are collinear iff the blue and purple points are collinear.

2184

Prove the red angles are congruent.

2183

The yellow shape is a square. Prove the red angle is double the blue angle.

2182

The blue angle is double the green angle. The blue line segment is double the green line segment. Prove the red line bisects a side of the yellow triangle.

2181

The blue line bisects the legs of the right triangle. Prove the red points are concyclic.

2180

Prove the blue angles are congruent iff the red angles are congruent.

2179

Prove the red point trisects the blue line segment.

2178

The green circles are tangent to the yellow circle. Prove the red line bisects the blue side of the triangle.

2177

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

2176

The yellow shape is a trapezoid. Prove the red angles are congruent.

2175

The blue shapes are squares. The yellow triangle is equilateral. Prove the red points are collinear.

2174

Find the measure of the red angle.

2173

The blue points are the midpoints of the sides of the green triangle. Prove the perimeter of the red polygon equals the perimeter of the green triangle.

2172

The yellow and blue shapes are squares. Prove the red and green points are collinear and the green point is the midpoint of the red points.

2171

The yellow shape is a parallelogram. The green line bisects the green angle. The blue line bisects the blue angle. The red line bisects the red angle. Prove the red and yellow lines are perpendicular.