Question

OAB is a sector of a circle with centre O.

OA= 8cm and AC is perpendicular to OB
the area of sector OAB is 8cm²(pie)
show that AC= 4root2cm​

Answer 1

To find the value of AC, we can use the formula for the area of a sector and the Pythagorean theorem. The length of AC is found to be 4√2 cm.

Step-by-step explanation:

To find the value of AC, we can use the formula for the area of a sector, which is given by:

Area of sector = (angle / 360) * (π * r2)

In this case, the area of the sector OAB is given as 8 cm2(π)

So, 8 = (angle / 360) * (π * 82)

Simplifying the equation, we get: angle = 360/(π * 82)

Since AC is perpendicular to OB, triangle OAC is a right triangle. Using the Pythagorean theorem, we can find the length of AC:

AC2 = OA2 - OC2

Since OA = 8 cm and OC = r, we have:

AC2 = 82 - r2

Substituting the value of r from the area equation, we get:

AC2 = 82 - (8/(2π))2

Simplifying the equation, we get:

AC2 = 64 - (64/(4π2))

Calculating the square root of both sides, we find:

AC = 4√2 cm