An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the radius, in inche
1 answer:
The radius of the circle is 3.12 inch.
<h3>What is isosceles triangle?</h3>A triangle having two sides of equal length. Additionally equal are the angles that face the equal sides. Triangle of isosceles. Having two identical sides and angles.
Calculation for the radius of the circle;
Consider the isosceles triangle ABC inscribed in a a circle (attached figure)
Sides AB = AC = 5 inches.
Side BC = 6 inches.
Join OB, OC and OA.
Draw perpendicular on BC from AD which passes from the centre O.
OD bisects BC at point D.
So, BD = DC = 3 inches.
In the right angled triangle ABC
AB² = AD² + BD²
5² = AD² + 3²
AD² = 16
AD = 4 inches.
Let the radius of the circle be r.
Then, OB = OC = OA = r
OD = AD - AO
OD = 4 - r
In the right angled triangle OBD;
OB² = OD² + BD²
r² = (4-r)² + 3³
On solving,
r = 25/8 = 3.12
Therefore, the radius of the circle comes out to be 3.12 inches.
To know more about the isosceles triangle, here
#SPJ4
You might be interested in