Coordinate Geometry and Circle (Class 10th)

The topics, Coordinate geometry and Circles hold great significance in the exam as you will get questions of more than 10 marks from these two sections. The chapter Circle is based on theorems, whereas Coordinate geometry has only three key formulae such as  Distance formula, Section formula and  Area of a Triangle. Let us see how to beat these two in upcoming exams.

In Circles, you need to memorize few very important theorems which will be applicable in most of the questions from this chapter. Few of them are as follows:

Theorem 1: The tangent at any point on the circle is perpendicular to the radius through the point of contact.

Theorem 2: The lengths of the tangents drawn from an external point to a circle are equal.

Theorem 3: The angle subtended by an arc at the centre of a circle is double the angle subtended by it at any point on the remaining part of the circle.

Theorem 4: Chords subtending equal angles at the centre of a circle are equal in length. The converse is also true.

Theorem 5: The sum of each pair of opposite angles of a cyclic quadrilateral is 180°. It’s converse is also true.

Theorem 6: The perpendicular drawn from the centre of a circle to a chord bisects the chord. The converse is also true.

Theorem 7: Equal chords are equidistant from the centre of the circle. The converse is also true.

Theorem 8: Perpendicular bisector of a chord always passes through the centre of the circle.

Theorem 9: Angles in the same segment of a circle are equal.

Here are few tips which can prove to be very useful for you to grab good score in these chapters:

1. It is very important that after reading the question, you should be able to know which theorem needs to be applied as sometimes questions are asked very cleverly. To identify the same, first of all draw a rough figure, and then try to apply the above theorems on it and write down the extracted information.
2. Most of the questions asked from this chapter, are expected to come from  in-circles, circles inscribed in the quadrilaterals or triangles, cyclic quadrilaterals and parallel tangents. You can identify these questions by drawing the figure.
3. The figure should be clear and labelled as it lends clarity to the solution and fetches you full marks.

For example:



In the above figure, every point is labelled and the radius is also shown.

4. In case of coordinate geometry, be careful about entering the correct coordinates in the formulae. To avoid this problem, always note down the coordinates first. For example, if the given points are  p (-3, 2) and Q(2, -5) then write them as as _x1 = – 3, _y1 = 2,_x2 = 2 and _y2 = – 5.
5. Do not forget to write units with the measures. Sometimes students forget to mention the symbol of angle, triangle, degree etc. which should not be done.

Taking care of these small things can prove to be very helpful for you to lead the race. So, be confident and go for it!

All the Best!

Team Meritnation