Mastering Geometry (For Class X)

Coordinate geometry: This chapter has three key formulae viz., distance formula, section formula and area of triangle.

Among all, the section formula is the most important from examination point of view. Some of the questions which have been asked previously are:

• Point P divides the line segment joining the points A (−1, 3) and B (9,8) such that AP/ PB = k/ 1. If P lies on the line x − y + 2 = 0, find the value of k.
• Find the ratio in which the point (2, y) divides the line segment joining the points A (−2, 2) and B (3, 7). Also find the value of y.

• The point R divides the line segment AB, where A(−4, 0) and B(0, 6) are such that . Find the coordinates of R.
• The point P which divides the line segment joining the points A(2,−5) and B(5, 2) in the ratio 2:3 lies in the quadrant ________.
• The mid-point of the segment AB is the point P (0, 4). If the coordinates of B are (−2, 3) then the coordinates of A are _______.
• If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5) then the coordinates of other end of the diameter are _______.
• If P  is the mid-point of the line segment joining the points A(−6, 5) and B (−2, 3) then the value of a is _________.

Expert tip: 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.

Circles: This chapter is based on theorems. The chapter covers the following theorems.

• *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.

(*Proof of this theorem is frequently asked in exams.)

Expert tips:

• 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 in some tricky manner. 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.
• Most of the questions asked from this chapter, are expected to come from circles inscribed in the quadrilaterals or triangles. You can identify these questions by drawing the figure.
• The figure should be clear and labelled as it lends clarity to the solution and fetches you full marks.

For example:

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!