ABC is a right triangle in which angle B=90 degree. If AB=8cm and BC=6cm, find the diameter of the circle inscribed in the triangle.
Answers
Answer anStep-by-step explanation in attachment.
I have used formula which can be used for radius in any type of triangle.
Diameter = 2*radius = 2*2 = 4cm
PLEASE MARK ME BRAINLIEST
Given : ABC is a right triangle in which angle B=90 degree.
AB=8cm and BC=6cm,
To find : the diameter of the circle inscribed in the triangle.
Solution:
Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.
AC² = AB² + BC²
=> AC² = 8² + 6²
=> AC² = 100
=> AC = 10
Area of Δ ABC = (1/2)AB * BC
Area of ΔABC = (1/2)(AB + BC + AC) * r
r = radius of inscribed circle
=> (1/2)(AB + BC + AC) * r = (1/2)AB * BC
=> ( 8 + 6 + 10) * r = 8 * 6
=> r = 2
Diameter = 2 * 2 = 4 cm
diameter of the circle inscribed = 4 cm
Another Way :
An Empirical formula to find Diameter of incircle of right angle triangle
AB + BC - AC ( Sum of perpendicular side - hypotenuse)
8 + 6 - 10
= 4 cm
Learn More :
abc is a triangle in which angle b is 90 degrees . if ab = 8 cm and bc ...
https://brainly.in/question/8641687
In the given figure a circle is inscribed in an equilateral triangle ABC ...
https://brainly.in/question/14745657
An equilateral triangle is inscribed in a circle of radius 7 cm. Find the ...
brainly.in/question/10153152
In the given fig. a circle is inscribed in a AABC. If AB=三9, BC = 10 ...
brainly.in/question/12231380