Question

Construct an isosceles triangle whose base is 8cm and altitude 4cm . Draw its circumcircle and measure its radius

Answer 1

Answer:

The measure of the radius of circumcircle is 4√2 cm  .

Step-by-step explanation:

Given as :

The measure of the base of isosceles Triangle = 8 cm

The measure of the altitude of isosceles Triangle = 4 cm

Let The radius of circumcircle drawn = r cm

According to question

ABC is isosceles Triangle having circumcircle with center O

So, OA = OC = OB = r

And measure of side BC = 8 cm

In figure ∠BOC = 90°

So, OB² + OC² = BC²

i.e r² + r² = 8²

Or, 2 r² = 64

Or, r² = $\dfrac{64}{2}$

i.e r² = 32

∴  r = √32

Or, r = 4√2  cm

So, The measure of the radius of circumcircle = r = 4√2 cm

Hence, The measure of the radius of circumcircle is 4√2 cm  . Answer

Answer 2

Step-by-step explanation:

The measure of the radius of circumcircle is 4√2 cm .

Step-by-step explanation:

Given as :

The measure of the base of isosceles Triangle = 8 cm

The measure of the altitude of isosceles Triangle = 4 cm

Let The radius of circumcircle drawn = r cm

According to question

ABC is isosceles Triangle having circumcircle with center O

So, OA = OC = OB = r

And measure of side BC = 8 cm

In figure ∠BOC = 90°

So, OB² + OC² = BC²

i.e r² + r² = 8²

Or, 2 r² = 64

Or, r² = 64}{2}

2

64

i.e r² = 32

∴ r = √32

Or, r = 4√2 cm

So, The measure of the radius of circumcircle = r = 4√2 cm

Hence, The measure of the radius of circumcircle is 4√2 cm . Answer