Learn Class 10 Math - Constructions

Construction refers to the concept that is related to shapes and figures. All the construction processes are the figures that we make with the help of different tools.

We have to draw the exact figures to make no mistakes in the angles.

Problem

Draw a right triangle wherein the sides other than hypotenuse with the length of 4 cm and 3 cm. And then make the other triangle whose sides are 5/3 times the relating sides of the given triangle.

Solution

Make a line segment PQ = 4 cm. And draw a line, i.e., PS with the 90-degree angle. Now, draw an arc with the 3 cm radius and make P the centre of the circle that intersects the PS with C. Join the two-line QR.

Here, QPR is the set triangle.

Draw an acute angle PX with PQ opposite the R vertex.

Now make the 5 points that are PP1 = P1P2= P2P3 = P3P4 = P4P5. Now, join the points P3 Q.

What to do when the centre of the circle is not known?

1. Make a secant PAB from the point P that intersects the circle at A & B.
2. Make AP to C, i.e., AP = PC.
3. Locate the midpoint of BC as M, & draw a semicircle.
4. Draw a perpendicular PD on BC intersecting the semicircle at D.
5. P = centre & radius, PD draws arcs intersecting the given circle at T & T’.
6. Join PT & PT’.

Then PT & PT’ are the tangents.