Question

In the below fig. ∠AOB = 90°, AC = BC, OA = 12 cm and OC = 6.5 cm. Find the area of ∆AOB.

Answer 1

Answer:

here is the answer

Step-by-step explanation:

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