Answer: A (I need to double check, Not sure about the answer)

AB is the diameter

Point O is the center of the circle

A: Area of triangle ABC?

B: twice the Area of triangle OBD?

Consider point C, the environment of circle which it faces (I think you name it arc) equals 180, why? Because AB is diameter and AB arc equals 180, so it’s facing angle which is C equals half of it, so C is 90 degrees.

A: Now area of ABC = AC*BC/2

We have:

A+B+C = 180 degrees x+2x+90 = 180 -> x = 30degrees

So angle O is 2x=60degrees. And as OB and OD are radiuses of circle, the OBD triangle is a equilateral. And thus, angles B and D equal (180-2x)/2 = 60degrees

B: The area of OBD*2 = 2* BD*H/2= BD*H

How much is H? we have all angles in OBD

sin B = H/OB -> H = sinB * OB = sin60 * OB = RADICAL3/2 *OB

A = AC*BC/2 sinB(2x)= AC/AB -> √3/2 = AC/AB -> AC = √3/2*AB -> A= √3/2*AB*BC/2

B = √3/2 * OB

A= √3/2*AB*BC/2

B = √3/2 * OB

So we omit √3/2 from both.

A -> AB*BC/2

B -> OB

We know OB = AB/2, so we substitute it in B:

A -> AB*BC/2

B -> AB/2

We omit AB/2 from both

And we will have

A -> BC

B -> 1

BC is bigger than 1, so A is bigger than B.

(Not sure about the answer)

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