1804

Prove the radius of the red circle equals the sum of the radii of the other circles.

1803

Prove the blue, red, and green points are collinear.

1802

Prove the measure of the red angle is invariant.

1801

Prove the red line segments are congruent.

1800

Each yellow circle is tangent to the blue circle (and black triangle). Prove the red lines and blue circle are concurrent.

1799

Prove the red lines perpendicular.

1798

Prove the red and blue triangles are similar.

1797

Prove the red and yellow points are concyclic.

1796

Prove the red line bisects the blue angle.

1795

Prove the red lines and blue circle are concurrent.

1794

Prove the red circles are congruent.

1793

The green and blue shapes are squares. Prove the red lines are concurrent.

1792

Prove $c^2 = 4ab$.

1791

The blue circles are congruent. Prove the ratio of the radius of a blue circle to the radius of the red circle is $4:13$.

1790

Prove the area of the red triangle is double the area of the blue triangle.

1789

Prove the red line is tangent to the yellow circle.

1788

The green line is an external angle bisector of the yellow kite. Prove the red line bisects the red angle.

1787

Prove the red and blue points are concyclic.

1786

Prove the red points are concyclic.

1785

Sides of the blue and green triangles are parallel. Prove the area of the red triangle is the geometric mean of the areas of the blue and grren triangles.

1784

Prove the area of the red triangle is half the area of the yellow hexagon.

1783

The green lines are perpendicular bisectors of the blue and orange line segments. Prove the red points are concyclic.

1782

Prove $OC = \sqrt{OA\cdot OB}$.

1781

Given $PC = \sqrt{PA\cdot PB}$. Prove $\displaystyle QC = \sqrt{QA'\cdot QB'}$.

1780

Prove the area of the red square equals the sum of the areas of the green and blue squares.

1779

Prove the area of the red rectangle equals the sum of the areas of the blue and green squares.

1778

Prove the red points are collinear.

1777

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

1776

The yellow triangle is isosceles. Prove $PC = \sqrt{PA\cdot PB}$.

1775

Prove the red radius bisects the red angle.

1774

Prove $PC = \sqrt{PA\cdot PB}$.

1773

Prove the red lines are perpendicular.

1772

Prove the blue vertex bisects the red line segment.

1771

Prove the red points are collinear.

1770

The red line is parallel to sides of the square. Prove the red and blue line segments are congruent.

1769

Prove $c = \sqrt{PA\cdot PB}$.

1768

Prove the red and blue triangles are similar.

1767

The sum of the blue angles is $180^\circ$ or $360^\circ$. Prove the red circles are concurrent.

1766

Prove the red shape is a rhombus.

1765

The blue altitude, green angle bisector, and red median quadrisect the yellow angle. Find the angles of triangle.

1764

Prove $c = \sqrt{PA\cdot PB}$.

1763

Prove the measure of the red angle is invariant.

1762

Given a square. Prove the areas of the blue triangle and red quadrilateral are the same.

1761

Prove the red line segments are congruent.

1760

The green angles differ by $60^\circ$. The blue angles differ by $60^\circ$. The orange angles differ by $60^\circ$. Prove the red triangle is equilateral.

1759

The yellow shape is a square. Prove $a = \frac{1}{\sqrt{2}}(c-d)$ and $b=\frac{1}{\sqrt{2}}(c+d)$.

1758

The red hexagon is equilateral with sides parallel to sides of the blue triangle. Prove the side length of the hexagon is $\dfrac{abc}{ab+bc+ca}$ where $a$, $b$, $c$ are the side lengths of the blue triangle.

1757

Prove the red points are concyclic.

1756

The blue points are the midpoints of the sides of the yellow triangle. The green triangles are equilateral. Find the measure of the red angle.

1755

Prove the red line segments are congruent.

1754

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

1753

Prove the red angles are congruent.

1752

Given a parallelogram. Prove the red angles are congruent and the blue angles are congruent.

1751

Prove the red line segments are congruent.

1750

Prove the red line bisects the blue angle.

1749

The red shape is a trapezoid. Prove the area of two blue squares equals the sum of the areas of the two green squares and the two congruent yellow rectangles. (Trapezoid law)

1748

The red shape is a parallelogram. Prove the area of the four yellow squares and the area of the two blue squares are the same. (Parallelogram law)

1747

Given $ab = cd$. Prove the red line segments are congruent.

1746

Prove the red lines are parallel.

1745

Prove the red side of the triangle bisects the blue chord.