Question

construct a pair of tangents to a circle of radius 4cm inclined at an angle of 45 degree

Answer 1

Answer:

please follow the steps .

Step-by-step explanation:

1)You need to first  draw a circle of 4 cm and mark its center as O.

2)Take any point A on the circle and join OA which is radius of circle =4cm.

3) Draw a perpendicular  to line segment OA at A.

4)Draw OB (radius ) making angle of 180-45=135 degree With OA.

5)Draw a line perpendicular to OB at B extend it.

6)Both the perpendicular lines from point A and B will intersect at point D .

Hence DA and DB are the tangents on the given circle making an angle of 45 degree

Answer 2

Construction:

• In context to the given question , we have to Construct a pair of tangents to a circle of radius 4cm inclined at an angle of 45 degree.

Given:-

Radius of a circle = 4cm

angle = 45°

Solution-

1)Firstly, draw a circle of radius 4 cm and mark its center as O.

2)Take any point A on the circle and join OA .

3) Draw a perpendicular  line segment AD to OA.

4) Take any point B, Draw OB (radius) making angle of 180°°-45°=135° With OA.

5) Draw a line perpendicular to OB and extend it to D.

6) Both the perpendicular lines from point A and B will intersect at point D

Now ,

In quadrilateral OADB

∠A = ∠B = 90°

∠O = 135°

∠D=?

∠A +∠B +∠O+∠D = 360° [angle sum property]

90° +90° + 135°+∠D = 360°

∠D = 360°- 135° - 180°

∠D = 45°

Therefore, it follows the given condition,

so,

DA and DB are the tangents on the given circle making an angle of 45°