Circles · वृत्त
Angle in a semicircle, cyclic quadrilateral, tangent length — learn the theorems and use them.
Circles games
Circle theorems · वृत्त
- Equal chords subtend equal angles at the centre and are equidistant from it.
- The perpendicular from the centre to a chord bisects it.
- The angle at the centre is twice the angle at the circle on the same arc.
- Angles in the same segment are equal; the angle in a semicircle is 90°.
- Opposite angles of a cyclic quadrilateral add to 180°.
- A tangent is perpendicular to the radius at the point of contact.
- Tangents from an outside point are equal: length = √(d² − r²).
For Class 9 and 10 (NCERT Mathematics 9 and 10, “Circles”). Answers computed by a program.
A one-page chart to stick on the wall, and a worksheet to practise.
Circle theorems
Centre angle = 2 × circle angle · semicircle 90° · cyclic opposite angles 180° · tangent ⟂ radius · tangent length √(d² − r²)
kheloaurseekho.in — free charts, games and worksheets
Circles — worksheet
Name: ____________________ Class: ______ Date: __________
1. ∠ at circle = 35°. ∠ at centre = ____
2. Cyclic quadrilateral: ∠A = 70°. ∠C = ____
3. r = 5 cm, point 13 cm from centre. Tangent length = ____
4. Prove that tangents from an external point are equal.
kheloaurseekho.in — free charts, games and worksheets
