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In the figure above, point O is the center of the circle, po
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06 Oct 2018, 15:10
06 Oct 2018, 15:10
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In the figure above, point O is the center of the circle, points A and C are located on the circle, and line segment BC is tangent to the circle. If the area of triangle OBC is 24, what is the length of AB?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Re: In the figure above, point O is the center of the circle, po
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15 Nov 2018, 00:38
15 Nov 2018, 00:38
1
I like this problem since it requires you to use a lot of things in relation to circles and triangles.
Since we are given that the area of the triangle is 24, we can plug it into the formula A=1/2bh, substituting A for 24, and the height for 8, which is given.
24 = 1/2 * 8 * b
24 = 4 * b
6 = b
By finding out the base is b, we are able to see that line OC is 6. From here, we want to find out the hypotenuse of the triangle.
If you know your Pythagorean Theorems, you would recognize the sides 6,8 are derivitives of 3,4,5 triangle, meaning that the 3rd side of 6,8 would be 10.
If not, then you could still calculate 6*6 + 8*8 = c*c.
36 + 64 = c*c
100 = c*c
10 = c. Note: I am not accounting for the negative square because it doesn't make sense here. Don't waste your time or energy.
Now that we know that side C or hypotenuse is 10, we can find out what Segment AB is. The problem states that points A & C are points on the circle. If OA is 6 and on the circle, it must also mean that OC is 6 because it is also on the circle. We essentially found out the "radius" of the circle.
From here, we make the formula AB = OB - OC
AB = 10 - 6
AB = 4
B is the correct answer.
Since we are given that the area of the triangle is 24, we can plug it into the formula A=1/2bh, substituting A for 24, and the height for 8, which is given.
24 = 1/2 * 8 * b
24 = 4 * b
6 = b
By finding out the base is b, we are able to see that line OC is 6. From here, we want to find out the hypotenuse of the triangle.
If you know your Pythagorean Theorems, you would recognize the sides 6,8 are derivitives of 3,4,5 triangle, meaning that the 3rd side of 6,8 would be 10.
If not, then you could still calculate 6*6 + 8*8 = c*c.
36 + 64 = c*c
100 = c*c
10 = c. Note: I am not accounting for the negative square because it doesn't make sense here. Don't waste your time or energy.
Now that we know that side C or hypotenuse is 10, we can find out what Segment AB is. The problem states that points A & C are points on the circle. If OA is 6 and on the circle, it must also mean that OC is 6 because it is also on the circle. We essentially found out the "radius" of the circle.
From here, we make the formula AB = OB - OC
AB = 10 - 6
AB = 4
B is the correct answer.
Re: In the figure above, point O is the center of the circle, po
[#permalink]
16 Nov 2018, 13:45
16 Nov 2018, 13:45
good question
