ABC is an isosceles triangle inscribed in a circle. If AB and AC equal to 2.5cm and BC is 14cm find the radius of the circle
To find the radius of the circle inscribed in the isosceles triangle ABC, we can use the property of an isosceles triangle that states: "If a triangle is isosceles, then the perpendicular bisector of the base of the triangle passes through the center of the circle."
Here's how we can find the radius of the circle:
1. Draw the isosceles triangle ABC with AB = AC = 2.5cm and BC = 14cm.
2. Draw the perpendicular bisector of BC, which will intersect BC at the midpoint D.
3. Since ABC is an isosceles triangle, AD is also the altitude of the triangle.
4. Using the Pythagorean theorem, we can find the length of AD. AD^2 = AB^2 - (BD/2)^2
- Substitute the given values: AD^2 = 2.5^2 - (14/2)^2
- Simplify: AD^2 = 6.25 - 49
- AD^2 = -42.75 (This means that the triangle is not possible with the given measurements. Please double-check the values)
Based on the given measurements, it seems there is an error or inconsistency. Please double-check the values provided for AB, AC, and BC before proceeding.