Question

draw a CIRCLE of radius 4cm and construct a pair of tangent to the CIRCLE such that the angle between the tangent is 60​

Answer 1

Answer:

ANSWER

Toconstruct−

ApairoftangentsPQ&PR,whichmakeanangleof60

o

atthepoint

oftheirintersectionP,toacircleofradius4cm&centreasO.

Tomeasure−

ThedistanceOP.

Construction−

I−AcirclewithcentreO&radius4cmisdrawn.

II−OQisjoinedwhenQisanypointonthecircle.

III−∠OQR=30

O

isdrawnandQRintersectsthecircleatR.

IV−CenteringQ&RandwithradiusQRtwoarcsaredrawn,

theyintersectatP.

V−PQ&PRarejoined.

PQ&PRaretherequiredtangents.

Justification−

PQ=QR=PR(byconstruction).

∴ΔPQRisequilateral

i.e∠PQR=∠QRP=∠RPQ=60

O

..........(i)

∴∠OQP=∠OQR+∠PQR=30

O

+60

O

=90

O

.

PQisatangenttothecircleatQ.

AgaininΔOQRwehave

OQ=OR(Radiiofthesamecircle).

∴∠OQR=30

O

=∠ORQ..........(ii)

So∠ORP=∠ORQ+∠QRP(fromi&ii)

⟹∠ORP=30

O

+60

O

=90

O

.

i.ePRisatangenttothecircleatR.

MeasureofOP=8cmbyactualmeasurement.

Ans−8cm.

Step-by-step explanation:

step of construction