Question

In the given figure, the radius of circle is 3cm.Find the perimeter of triangle ABCD.

Answer 1

Answer:

The perimeter of triangle ABCD is 36 cm.

Step-by-step explanation:

Given : In the given figure, the radius of circle is 3cm.

To find : The perimeter of triangle ABCD.

Solution :

In triangle BOC,

let D be mid point of BC

So, in triangle ODC (right triangle since BC is tangent)

OC = hypotenuse = 3√5 cm

OD = radius = 3 cm (given)

Applying Pythagoras theorem,

$DC^2 = (3\sqrt5)^2-3^2 = 45 - 9 = 36$

DC = 6 cm

So, BC = 2(DC) =2(6)= 12 cm

Now, the triangle ABC is equilateral since,

$\angle BOC=\frac{360}{3}=120$

In triangle BOC,

$\angle OCB=\angle OBC$  (since OB = OC)

$\angle OCB+\angle OBC=180-\angle BOC$

$\angle OCB+\angle OBC=180-120$

$\angle OCB+\angle OBC=60$

Hence $\angle OCB=\angle OBC=30$

Now,

$\angle ACO=\angle OCB$ ( OC is angle bisector)

$\angle ACO=30$

$\angle ACO+\angle OCB=60=\angle C$

Similarly $\angle B =60$

Therefore, $\angle A =60$

Hence its an equilateral triangle with side BC = 12cm

So, The perimeter is 12+12+12 = 36 cm