# 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??

Dear Student!

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 is cm.

Cheers!

• 38

please check your question, it seems wrong. how can tangent to the circle makes 30 degree with line passing through center??tangent always make 90 degree with line passing through center.

• 0

add me if u don't have problem

• 0

but this is what my teacher gave me!!

• 4

ok, i m telling u

• 0

or is it like an extended diameter and the tangent and this line at the point of intersection make 30degrees?

• -2

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.

• -5

it will be tan 30 = 3/x i don't remember value of tan 30 my ans is wrong but u can get value without measuring it.

• -1

it will be tan 30 = 3/x. and my ans may be wrong, i don't remember value of tan 30 degree

• 2

tan 30 = 3/x => x= 3 tan 30 = 1.732 cm appox....

• -1

byeeeee

• -1
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