Question
A circle has an area equal to 25 pi sq.cm. Its diameter AB coincides with one of the sides of triangle ACB in which the vertex C lies on the circle. If the triangle has an area equal to 11 sq.cm, find its perimeter.
Please include solution. Thanks.
Please include solution. Thanks.
Answers
drwls
The circle radius is 5 cm. That comes from the area.
The triangle ACB is a right triangle with AB as a diameter. The length of AB is 10 cm, since it is a diameter
(AC)^2 + (BC)^2 = (AB)^2 = 100
Area = (1/2)(AB)*(BC) = 11
(AC)*(BC) = 22
(BC)=22/(AC)
(AC)^2 + 484/(AC)^2 = 100
Solve for AC. The short side is about 2.3. Then get BC and the perimenter.
Then get BC
The triangle ACB is a right triangle with AB as a diameter. The length of AB is 10 cm, since it is a diameter
(AC)^2 + (BC)^2 = (AB)^2 = 100
Area = (1/2)(AB)*(BC) = 11
(AC)*(BC) = 22
(BC)=22/(AC)
(AC)^2 + 484/(AC)^2 = 100
Solve for AC. The short side is about 2.3. Then get BC and the perimenter.
Then get BC