Draw a circle of radius 3.5 cm. Draw two tangents to the circle such that they include an angle of 120 degree.
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Answers
Answer:
Steps of construction
Step I. Draw a circle of any convenient radius with O as centre.
Step II. Take a point A on the circumference of the circle and join OA. Draw a perpendicular to OA at point A.
Step III. Draw a radius OB, making an angle of 90° with OA.
Step IV. Draw a perpendicular to OB at point B Let both the perpendicular intersect at point P
Step V. Join OP
PA and PB are the required tangents, which make an angle of 45° with OP.....
Answer:
Follow the given steps to construct a pair of tangents.
Step 1: Take a point O on the plane and draw a circle of radius OA = 3.5 cm
Step 2: Draw ∠AOB = ∠AOC = 30° at O.
Step 3: Draw BX ⊥ OB and CX ⊥ OC at B and C
respectively. BX and CS intersects at X.
Here, BX and CX are two tangents to the circle inclined to each other at 120°.
Justification:
∠XOB = 30°
∠OBX = 90°
In ΔBOX,
∠XOB + ∠OBX + ∠BXO = 180°
∴ 30° + 90° + ∠BXO = 180°
⇒ ∠BXO = 180° – 120° = 60°
Similarly, ∠CXO = 60°
∴ ∠BXC = ∠BXO + ∠CXO = 60° + 60° = 120°
REFER TO THE ATTACHMENT ALSO....
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