Triangle Geometry Theorems

Question 1

If a line segment is drawn from the centre of a circle to the midpoint of a chord, then this line segment is perpendicular

Answer 1

Mid-chord theorem

Question 2

If two chords intersect, the product of the lengths of the intervals on one chord equals the product of the lengths of the other

Answer 2

Intersecting chord theorem

Question 3

The angle between the radius and the tangent at the point of tangency is a right angle

Answer 3

Tangent-radius theorem

Question 4

The angle between a tangent and a chord is equal to any angle in the alternate segment

Answer 4

Angle in alternate segment theorem

Question 5

The lengths of tangents from an external point to a circle are equal

Answer 5

Lengths of tangent theorem

Question 6

If a quadrilateral is cyclic, then the opposite angles are supplementary

Answer 6

Cyclic Quadrilateral theorem

Question 7

If two chords are congruent, then they subtend angles of equal size at the centre

Answer 7

Congruent Chord Theorem