Questions on Geometry: Circles and their properties answered by real tutors!

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Question 148486: The diameter of circle AOB is 12, Triangle ABC is inscribed in the circle, angle A = 45. In cm squared what is the area of Triangle ABC,
a) 18
b) 108
c) 144
d) 36
or e) 72 : The diameter of circle AOB is 12, Triangle ABC is inscribed in the circle, angle A = 45. In cm squared what is the area of Triangle ABC,
a) 18
b) 108
c) 144
d) 36
or e) 72
Answer by mangopeeler07(445) (Show Source):
You can put this solution on YOUR website!
If in your diagram, two legs of the right triangle are congruent, then each leg is 6, because they are probably half the diameter long.

Area of triangle=(1/2)bh
b=6
h=6

Area of this triangle=1/2(6x6)
Or 1/2(36)

Area=18

If not, then the longest side is probably 12, making the height a radius, or 6.

Area of triangle=(1/2)bh
b=6
h=6

Area of this triangle=1/2(12x6)
Or 1/2(72)

Area=36

I gave you two answers because I don't know what your diagram looks like.
Question 148486: The diameter of circle AOB is 12, Triangle ABC is inscribed in the circle, angle A = 45. In cm squared what is the area of Triangle ABC,
a) 18
b) 108
c) 144
d) 36
or e) 72 : The diameter of circle AOB is 12, Triangle ABC is inscribed in the circle, angle A = 45. In cm squared what is the area of Triangle ABC,
a) 18
b) 108
c) 144
d) 36
or e) 72
Answer by jim_thompson5910(9403) (Show Source):
You can put this solution on YOUR website!
First draw the inscribed triangle in the circle and label all of the sides and angles given.

Now draw in the radius from the center O to the angle ACB. Since the inscribed angle BAC is 45 degrees, this means that the central angle BOC is 90 degrees (remember the central angle is double the inscribed angle when they cut the same arc length). Now since the diameter is 12, this means that the radius is 6. So let's draw all of this info in:

Since OC is perpendicular to AB, this means that OC is the height and AB is the base

Now let's use the area of a triangle formula to find the area

Start with the known formula

Plug in and

Multiply

Reduce

So the area of the triangle is 36 square units. This means that the answer is choice d)