Radii

Geometry Level 3

Consider all triangles with an inradius of 3.

What is the minimum length of the circumradius of these triangles?

The answer is 6.

1 solution

Shabarish Ch
Dec 8, 2014

Using the inequality , $R \geq 2r$ , where R stands for circumradius, and r stands for inradius, we get 6 as the answer..

brother, i took a right triangle ..... since a triangle with sides 3,4,5 as inradius =1, a triangle sides whose inradius =3 are 9,12,15 ....... having drawn the circumcircle, i found the hypotenuse to b the diameter ..... so circumradius = 7.5 cm ...... this also satisfies your inequality ... then y is my answer wrong???

Ganesh Ayyappan - 6 years, 6 months ago

Because it asks for minimum value, in an equilateral triangle with in radius 3 you will get circumradius as 6....

Shabarish Ch - 6 years, 6 months ago

how r u sure value is only 6 ..... there are many nos. more than 3 ..... how u solved it .... can u tell step-by-step??

Ganesh Ayyappan - 6 years, 6 months ago

@Ganesh Ayyappan – So sorry, I forgot to write the 2 in the inequality by mistake, now you can see clearly how I got 6...

Shabarish Ch - 6 years, 5 months ago

@Shabarish Ch – even in that case 7.5>6 ...... i wish to get a proper soln. on how u get 6 = R .....

Ganesh Ayyappan - 6 years, 5 months ago

@Ganesh Ayyappan – It asks for minimum value, the value of R can be 6 (in equilateral triangle) or 7.5 (in your triangle), so the minimum value is 6 here. And how do I know that R cannot be less than 6? The above inequality tells me.

Shabarish Ch - 6 years, 5 months ago

@Shabarish Ch – brother .... thanks a lot .....

Ganesh Ayyappan - 6 years, 5 months ago

@Ganesh Ayyappan – You're welcome

Shabarish Ch - 6 years, 5 months ago

Radii

The answer is 6.

1 solution

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