Question

angle between the tangent drawn to a circle of radius 3cm from an external point is go thrn the lenght of each tangent is​

Answer 1

Step-by-step explanation:

Ap=BP ....(length of tangents from external point to circle are equal)

∠A=∠B=90

o

.... (Tangent is ⊥ to radius)

OP=OP .... (common side)

∴△AOP≅△BOP ....(RHS test of congruence)

∠APO=∠BPO=30

o

→c.a.c.t

∠AOP=∠BOP=60

o

→c.a.c.t

△AOP is 30

o

−60

o

−90

o

triangle.

∴△AOP,

cos60=

OP

OA

OP=

2

1

a

=2a

Answer 2

Suppose O be the centre of the circle and PA and PB be the two tangents drawn from P to the circle so that angle APB= 60°

Join OP,OA and OB.

Then angle OAP= angle OBP = 90° and

angle OPA = angle OPB = 30°

OA = OB = 3 cm.

In the right triangle OAP,

OA/AP = tan 30° => 3/AP = 1/√3

So AP= 3√3cm or3×1.732=5.196 cm

So length of each tangent = 5.196 cm.