3. Draw circle of radius 6cm and draw
tangent to this circle making an angle of
30 degree with a line passing through the centre
Answers
Step-by-step explanation:
Follow the given steps to construct a tangent to the circle.
Step1: Take a point O and draw a circle of radius, OA = 6 cm.
Step2: Produce OA to B such that OA = AB = 6 cm
Step3: Taking A as centre, draw a circle of radius AD = AB = 6 cm. Let it intersect the circle in P.
Step4: Join BP
BP is the required tangent to the circle.
OA = OP (Radius of circle with centre O)
AP = OP (Radius of circle with centre A)
∴ OA = OP = AP
Hence, ΔOAP is an equilateral triangle.
∴ ∠OAP = ∠AOP = ∠OPA = 60°
OP ⊥ PB (Radius is perpendicular to tangent at the point of contact)
∴ ∠OPB = 90°
In ΔOBP
∠BOP + ∠OBP + ∠OPB = 180°
∴ 60° + ∠OBP + 90° = 180°
⇒ ∠OBP = 180° – 150° = 30°
Length of tangent, PB =
Thus, the length of the tangent, PB iscm.
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3. Draw circle of radius 6cm and draw
tangent to this circle making an angle of
30 degree with a line passing through the centre
