1288

Prove as the blue point varies on the circle, the length of the red line segment remains constant.

1287

Prove the red shape is a parallelogram.

1286

Prove the red lines are parallel.

1285

Prove the red shape is a parallelogram.

1284

Prove the red lines are perpendicular.

1283

Prove $c=\sqrt{ab}$.

1282

The green point is the orthocenter of the green triangle. The blue point is the orthocenter of the blue triangle. Prove the red triangle is similar to the black triangle.

1281

Prove $R=\dfrac{ab}{2h}$.

1280

Prove $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=\dfrac{1}{r}$.

1279

Prove the red lines are perpendicular.

1278

Prove the red lines are parallel.

1277

Prove the red line segments are congruent.

1276

Prove the red lines are perpendicular.

1275

Prove the red lines are perpendicular.

1274

Prove the red line segments are congruent.

1273

Prove the red line is parallel to a side of the black triangle.

1272

Prove the red area is half the area of the black triangle.

1271

Prove the red line segments are congruent.

1270

Prove the red angles are congruent.

1269

Find the measure of the red angle.

1268

Find the measure of the red angle.

1267

Prove the sum of the red angles is $540^\circ$.

1266

Prove the sum of the red angles is $180^\circ$.

1265

The yellow circles are congruent. Prove the red angles are congruent.

1264

Prove $a:b=r:s$.

1263

Prove $c=\sqrt{ab}$.

1262

The green arcs are similar to the blue arc. Prove the red points are collinear.

1261

Prove the red angles are supplementary.

1260

Find the measure of the red angle.

1259

Prove the red line segments are congruent.

1258

Prove the red points are collinear.

1257

Prove the blue quadrilateral is tangential.

1256

Prove $\sqrt{a}+\sqrt{b}=\sqrt{c}$.

1255

The green rectangles are congruent. Prove $a=2b$.

1254

Prove the red lines are perpendicular.

1253

Prove the red points are concyclic.

1252

Prove the area of the red square equals the area of the blue rectangle.

1251

Prove the red triangle is equilateral.

1250

Given a regular heptagon. Prove $\dfrac{a^2}{b^2}+\dfrac{b^2}{c^2}+\dfrac{c^2}{a^2}=6$ and $\dfrac{b^2}{a^2}+\dfrac{c^2}{b^2}+\dfrac{a^2}{c^2}=5$.

1249

Given a regular pentagon. Prove $\dfrac{a^2}{b^2}+\dfrac{b^2}{a^2}=3$.

1248

Prove the red line segments are congruent.

1247

The black shape is a rectangle. Prove the red line bisects the blue angle.

1246

Prove $\dfrac{p}{q} = \dfrac{ab+cd}{ad+bc}$ (Ptolemy's second theorem).

1245

The blue shape is a square. The green triangle is equilateral. Find the measure of the red angle.

1244

Prove the red points are collinear.

1243

The blue shape is a square. Prove $\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{1}{c}$.

1242

The triangle is equilateral. Prove $a+b+c=p+q+r$.

1241

Prove the red points are collinear.

1240

Prove the red line segments are congruent.

1239

Prove the red lines are concurrent.

1238

The red points are midpoints of the green line segments. Prove the color points are concyclic.

1237

Prove $\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{4a}{c^2}=\dfrac{4b}{d^2}$.

1236

Prove $\dfrac{1}{\sqrt{a}} + \dfrac{1}{\sqrt{b}} = \dfrac{1}{\sqrt{c}}$.

1235

Prove $a=b$ and $c:d=3:1$

1234

The black shape is a parallelogram. Prove the red area equals the yellow area.

1233

The blue shapes are squares. Prove the red lines are perpendicular.

1232

The red and yellow points quadrisect the perimeter of the triangle. Prove the red and blue points are collinear.

1231

Prove the red points are collinear.

1230

The black triangle is isosceles. Prove the red points are collinear.

1229

The blue angle is double the green angle. Prove $\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{2}{c}$.

1228

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

1227

The blue shape is a rhombus. Prove the red shape is a square.

1226

Prove the red points are concyclic.

1225

Prove the red triangles are similar.

1224

The yellow points are the midpoints of the sides of the triangle. Prove the red lines are concurrent.

1223

The blue line is a median. The red line is an altitude. The green line is an angle bisector. Prove they are concurrent.

1222

Prove $a^2:b^2=c:d$

1221

Find the measure of the red angle.

1220

Prove $c=\sqrt{ab}$.