Competition Math Arena
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Geometry

Right-triangle area

Area of a right triangle from its two legs.

Practise

Rectangle perimeter

Perimeter of a rectangle from width + height.

Practise

Missing triangle angle

Find the third angle of a triangle.

Practise

Pythagorean hypotenuse

Find the hypotenuse of a right triangle.

Practise

Pythagorean leg

Find the other leg from the hypotenuse + one leg.

Practise

Triangle area (Heron)

Area of a triangle from its three sides via Heron's formula.

Practise

Trapezoid area

Area of a trapezoid from its parallel sides + height.

Practise

Regular polygon angle

Find an interior angle of a regular polygon.

Practise

Isosceles apex angle

Find the apex angle from a base angle (angle chasing).

Practise

Isosceles exterior angle

Chase the base angle, then the exterior angle.

Practise

Cyclic quadrilateral

Opposite angles of a cyclic quadrilateral sum to 180°.

Practise

Angle between parallels

Angle at a point between two parallel lines (auxiliary line).

Practise

Inscribed & central angle

Inscribed angle = half the central angle on the same arc.

Practise

Double isosceles chase

Chase angles through two isosceles triangles (180 − 3B).

Practise

Star point angles

The five point-angles of a 5-pointed star sum to 180°.

Practise

Two tangents to a circle

Angle between two tangents = 180° − central angle.

Practise

Incentre angle (BIC)

angle BIC = 90° + A/2 (internal bisectors).

Practise

Orthocentre angle (BHC)

angle BHC = 180° − A (altitudes).

Practise

Circumcentre angle (BOC)

angle BOC = 2A (central = twice inscribed).

Practise

Angle bisector foot

angle ADB = 90° + (C − B)/2 for the bisector from A.

Practise