Basics of circles and related theorems: 1. Equal chords in equal circles are equidistant from the centres. 2. Chords in a circle that are equidistant from the centre are equal. 3. The perpendicular from the centre of a circle to a chord bisects the chord. 4. The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord. 5. Tangents to a circle from an external point are equal. 6. The angle at the centre of a circle is double the angle at the circumference standing on the same arc. 7. Angles in the same segment of a circle are equal. 8. The opposite angles of a cyclic quadrilateral are supplementary. 9. The angle of a semi-circle is a right angle. 10. The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.

The topic is Circle Theorems. All questions are descriptive and detailed explanations of answers are given by using pictures. This topic is useful for Grade 8,9&10 of IGCSE and Cambridge Students. It is very helpful for preparing for board exams.

A two-dimensional Cartesian coordinate system is formed by two mutually perpendicular axes. The axes intersect at point O, which is called the origin. In the right-handed system, one of the axes (x-axis) is directed to the right, the other y-axis is directed vertically upwards

Two-dimensional coordinate geometry deals with the x and y coordinates which are represented in a coordinate plane or Cartesian plane. A point p(x,y) is represented in the X-Y plane, where x and y are the coordinates of the point, as shown below. 'O' is known as origin whose coordinate is (0,0).