Draw a circle of radius 6cm. draw a tangent to the circle making 30degree with the line passing through the centre. measure the lenght of the tangent.
Can someone plz tell me the steps of construction to do this??
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°
∠BOP + ∠OBP + ∠OPB = 180°
∴ 60° + ∠OBP + 90° = 180°
⇒ ∠OBP = 180° – 150° = 30°
Length of tangent, PB =
Thus, the length of the tangent, PB is cm.
first draw circle of 6 cm, draw any line from cricle from cricle and where it touches cricle draw a tangent (90 degree from that line). now draw a line from center to that tengent at angle 60 degree from previous line of circle. as tangent=90 degree, and other angle is 60 degree it will meet to tengent at 30 degree. now measure length. it will be tan 30 = 3/x => 1/2 = 3/x => x=6 cm answer.