# Tamil Nadu Board Class 10 Solutions for Mathematics – Practical Geometry (English Medium)

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** The study of Geometry is concerned with knowing
properties of various shapes and**

**structures. Arithmetic and Geometry were considered
to be the two oldest branches of**

**mathematics. Greeks held Geometry in high esteem
and used its properties to discuss**

**various scientific principles which otherwise would
have been impossible. Eratosthenes**

**used the similarity of circle to determine the
circumference of the Earth, distances**

**of the moon and the sun from the Earth, to a
remarkable accuracy. Apart from these**

**achievements, similarity is used to find width of
rivers, height of trees and much more.**

**Ex 4.10 **Construct
a triangle similar to a given triangle PQR with its sides equal to of
the corresponding sides of the triangle PQR (scale factor <
1).

**Ex 4.11 **Construct
a triangle similar to a given triangle PQR with its sides equal to

**EXERCISE - 4.1**__ __

**10. **Construct
a triangle similar to a given triangle PQR with its sides equal to

**11. **Construct
a triangle similar to a given triangle LMN with its sides equal to

**12. **Construct
a triangle similar to a given triangle ABC with its sides equal to

**13. **Construct
a triangle similar to a given triangle PQR with its sides equal to of the corresponding sides of the triangle
PQR. (Scale factor

Example 4.17 : Construct a ΔPQR in which PQ=8cm, ÐR=60°and the median RG from R to PQ is 5.8cm.Find the length of the altitude from R to PQ.

Example 4.18 : Construct a triangle ΔPQR such that QR=5cm, ÐP=30° and the altitude from P to QR is oflength 4.2 cm.

Ex 4.19 Draw a triangle ABC of base BC=8cm, ÐA=60° and the bisector of ÐA meets BC at D suchthat BD=6cm.

**EXERCISE - 4.2**

11. Construct a ΔPQR which the base PQ=4.5cm, ÐR=35° and the median from R to RG is 6cm.

12. Construct a ΔPQR in which QR=5cm, ÐP=40° and the median PG from P to QR is 4.4cm. Find the length of
the altitude from P to QR.

13. Construct a ΔPQR such that QR=6.5cm, ÐP=60° and the altitude from P to QR is of length 4.5cm.

14. Construct a ΔABC such that AB=5.5cm, ÐC=25° and the altitude from C to AB is 4cm.

15. Draw a triangle ABC of base BC=5.6cm, ÐA=40° and the bisector of A meets BC at D such that CD=4cm.

16. Draw ΔPQR such that PQ=6.8cm, vertical
angle is 50° and the bisector of the vertical angle meets the base at D where
PD=5.2cm.

**Example 4.31 : Draw a circle of diameter 6cm from a point P, which is 8cm away from its center. Draw the two tangents PA and PB to the circle and measure their lengths.**

**EXERCISE - 4.3**

14. Draw the two tangents form a point which is 10cm away from the centre of a a circle of radius 5cm.Also, measure the lengths of the tangents.

16. Draw the two tangents from a point which is 5cm away from the centre of a circle of diameter 6cm. Also, measure the length of the tangents.

17. Draw the tangents to the circle from the point p having radius 3.6cm , and centre at 0. Point P is at a distance 7.2cm from the centre.

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