Draw a pair of tangents to a circle of radius 5cm which are inclined to each other at an angle 90
Answers
Answer:
We know that radius of the circle is perpendicular to the tangents (∠OPN = ∠ORN = 90°)
Sum of all the 4 angles of quadrilateral = 360°
Angle between the radius (∠POR) = 360° – (90° + 90° + 60°) = 120°
GIVEN: A circle of radius 5 cm and a pair of tangents inclined to each other at an angle of 60°.
STEPS OF CONSTRUCTION:
1.Draw a circle with OS centre and radius 6 centimetre.
2. Draw any diameter POQ of the circle.
3.Draw the radius over means the circle at are such that ∠QOR = 60°.
4.Draw PD ⟂ PQ & RE ⟂ OR.
Let PD &RE intersect each other at point N. Then NP & NR are the required tangents to the given circle inclined to each other at an angle of 60°.
JUSTIFICATION:
By construction, ∠OPN = 90° and OP is radius PN is tangent to the circle.
Similarly, NR is a tangent to the circle.
Now, ∠POR = 180° - 60° = 120°
[POQ is a straight line and ∠QOR= 60°]
In quadrilateral OPNR,
∠OPN = 90°, ∠POR = 120° & ∠ORN = 90°.
∠PNR= 360° - ( 90° +120° +90°)
∠PNR = 360° 300° = 60°
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