Basic Concepts in Geometry
- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Theorem of remote interior angles of a triangle
- Congruence of Triangles
- Isoscles Triangle Theorem
- Property of 30-60-90 Triangle Theorem
- Median of a Triangle
- Perpendicular bisector Theorem
- Angle bisector theorem
- Properties of inequalities of sides and angles of a triangle
- Similar Triangles
Constructions of Triangles
Surface area and volume
Properties of congruent chords:
- A perpendicular drawn from the centre of a circle on its chord bisects the chord.
The segment joining the centre of a circle and the midpoint of its chord is perpendicular to the chord.
Relation between congruent chords of a circle and their distances from the centre
Congruent chords of a circle are equidistant from the centre of the circle.
The chords of a circle equidistant from the centre of a circle are congruent.
Radius of a circle with centre O is 41 units. Length of a chord PQ is 80 units, find the distance of the chord from the centre of the circle.
In the given figure, centre of two circles is O. Chord AB of bigger circle intersects the smaller circle in points P and Q. Show that AP = BQ
Distance of chord AB from the centre of a circle is 8 cm. Length of the chord AB is 12 cm. Find the diameter of the circle.
Radius of a circle is 34 cm and the distance of the chord from the centre is 30 cm, find the length of the chord.
Diameter of a circle is 26 cm and length of a chord of the circle is 24 cm. Find the distance of the chord from the centre.
Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle ?
In a circle with radius 13 cm, two equal chords are at a distance of 5 cm from the centre. Find the lengths of the chords.