Question

How do I find anything without knowing the degree of the shape?

Answer 1

I don't personally know much about cyclic quadrilaterals, but I do know that the angle opposite to the central angle is half the size of the central angle. So angle ∠BCA is 45º. Sorry, but I can't answer the other questions :(

Answer 2

Explanation:

Notice that BCA is an inscribed angle. It intercepts the arc AB. Since Arc AB is 90, Angle BCA is half of that, which is 45.

The measure of Arc AB can be found using the arc length formula, Where a is the central angle, which is 90 degrees.

`s = r ( ( \alpha )/(180) )\pi`

`s = 7( (90)/(180) )\pi) = (7\pi)/(2)`

The measure of Arc ACB can be found by the arc length formula.

Arc ACB central angle is

`270`

So

`s = 7( (270)/(180) )\pi = (21)/(2) \pi`

The shaded area can be found by using the area of sector formula

`c = \pi {r}^(2) ( ( \alpha )/(360) )`

Where alpha is the central angle, which is 270

`c = \pi(49)( 1.5) = 73.5\pi`