I’m Up and Down, and Round and Round - Quick Look Revision Guide
Your 1-page summary of the most exam-relevant takeaways from Ganita Manjari.
This compact guide covers 20 must-know concepts from I’m Up and Down, and Round and Round aligned with Class 9 preparation for Mathematics. Ideal for last-minute revision or daily review.
Complete study summary
Essential formulas, key terms, and important concepts for quick reference and revision.
Key Points
Define a Circle.
A circle is defined as a set of points that are equidistant from a center point.
Circle's Properties.
All points on a circle are at equal distance (radius) from the center.
Chord Definition.
A chord is a line segment with both endpoints on the circle; a diameter is a chord through the center.
Circle Symmetries.
A circle has infinite lines of symmetry and complete rotational symmetry.
Perpendicular Bisector and Circles.
The centers of all circles through points A and B lie on the perpendicular bisector of AB.
Unique Circle Theorem.
Three non-collinear points A, B, and C define a unique circumcircle with circumcenter O.
Equal Chords Property.
Equal chords of a circle subtend equal angles at the center, and vice versa.
Perpendiculars from Circle Center.
The perpendicular from center C to a chord bisects the chord.
Chords and Distance.
Chords of equal length are at the same distance from the center of the circle.
Longer Chord Closer.
In a circle, the longer chord is closer to the center than the shorter chord.
Angles Subtended by Arcs.
The angle at the center is twice the angle subtended on the circumference by the same arc.
Angle in a Semicircle.
The angle subtended by a diameter at any point on the circle is 90°.
Cyclic Quadrilaterals.
A quadrilateral inscribed in a circle has opposite angles that sum to 180°.
Concyclic Points Theorem.
If four points subtend equal angles at two other points, they are concyclic.
Circle and Lines.
No chord in a circle can be longer than its diameter.
Finding Circle Radius.
Use the distance to the chord and the radius to calculate the length of a chord.
Using Cyclometric Properties.
Utilize cyclic properties to determine if points are concyclic or to calculate angles.
Area of Cyclic Quadrilaterals.
Use Brahmagupta’s formula to find the area of cyclic quadrilaterals.
Angles in Circle Segments.
Angles subtended by arcs in the same segment are equal.
Chords and Isosceles Triangles.
The triangle formed by a chord and the center of the circle is isosceles.
