Question

Construct a pair of tangents to a circle of radius 3 centimetre with are included to each other at an angle of 60

Answer 1

Answer:

PQ and PR are the tangents to the given circle. If they are inclined at 60°,then

QPO = OPR = 30°

Hence, POQ = POR = 60° Consider ∆QSO,

QOS = 60°

OQ = OS (radius)

So, OQS = OSQ = 60°

∆QSO is an equilateral triangle.

So QS = SO = QO = radius

PQS = 90° - OQS = 90° - 60° = 30°

QPS = 30°

PS = SQ (isosceles triangle)

Hence PS = SQ = OS (radius)

Now the tangents to the given circle can be drawn as follows:

1. Draw a circle of 3 cm radius and with centre O.

2. Take a point S on circumference of this circle. Extend OS to P such that OS =PS.

3. Midpoint of OP is S. Draw a circle with radius OS and centre as S.

Let it intersect our circle at Q and R. Join PQ and PR. PQ and PR are requiredtangents.

Answer 2

Answer:

Step-by-step explanation: