Question

Draw a pair of tangentd to a circle of radius 4.5 cm, which are inclined to each other at an anglr of 45°

Chapter : Construction

Answer 1

First of all refer to the rough diagram

we have to find out the value of x.

In PQOR

$45 + 90 + x + 90 = 360 \\ \\ 225 + x = 360 \\ \\ x = 360 - 225 \\ \\ x = 135$

So now be steps for construction:-

1) Take the distance of 4.5 cm in compass.

2) Draw a circle of radius 4.5 cm.

3) Mark the centre point as O.

4) Make a line segment from O on the circle at point Q.

5) Now make the angle of 135° at point O and join it at the circle on point R.

6) At point Q and R make the angle of 90°.

7) Extend both the sides until they meet each other at point P.

8) Join PQ and PR.

9) The angle PQR will surely be of 45°.

Hope it may help you.

Answer 2

Hii

Here is your answer -

Steps of construction

1. draw a circle of 4.5cm
2. Join OB
3. Construct an angle AOB whose angle AOB = 135°
4. Join OA
5. construct angle 90°at A&B
6. Mark a point P where the ray from B&A intersect
7. Angle APB = 45° is the required angle