Question

A triangle has two 13-cm sides and a 10-cm side. The largest circle that fits inside this triangle meets each side at a point of tangency. These points of tangency divide the sides of the triangle into segments of what lengths? What is the radius of the circle?

Answer 1

Answer:

$r=3.33 cm$

$d_{a}=5 cm$

Step-by-step explanation:

Let's use the radius equation to a circle inscribed into a triangle.

$r=\sqrt{\frac{(s-a)(s-b)(s-c)}{s}}$

$s=\frac{a+b+c}{2}$

In our case a = 13 mc, b = 13 cm  and c = 10 cm

Then, s will be s = 18 cm

Then the radius will be:

$r=\sqrt{\frac{(18-13)(18-13)(18-10)}{18}}=3.33 cm$

Now, the distance from the vertex to the nearest touchpont is given by:

$d_{a}=\frac{1}{2}(a+c-b)=5$

This value is the same for each side.

I hope it helps you!