Angle = 90 degree Ac = BC ,OA= 12cm and OC = 6.5 find the area of tri
angle aob
Answers
Answered by
12
Note that C is the mid-point of AB. Hence AC = AB. Also angle AOB is 90 degree.
Hence if you imagine the circum-circle of triangle AOB, you will find that AB is the diameter. This is because angle in a semi- circle is 90 degree. Hence AB is the diameter and C being is the mid-point of the diameter is also the center of the circum-circle.
OC being the radius must be equal to half of AB. Hence AB = 2OC = 25 cm.
Hence, by Pythagoras theorem OB =
√25^2 - 7^2 = 24 cm
Area of triangle AOB =
AO×AB/2 = 7×24/2 = 84 cm^2
Hence if you imagine the circum-circle of triangle AOB, you will find that AB is the diameter. This is because angle in a semi- circle is 90 degree. Hence AB is the diameter and C being is the mid-point of the diameter is also the center of the circum-circle.
OC being the radius must be equal to half of AB. Hence AB = 2OC = 25 cm.
Hence, by Pythagoras theorem OB =
√25^2 - 7^2 = 24 cm
Area of triangle AOB =
AO×AB/2 = 7×24/2 = 84 cm^2
Similar questions