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Guest
Guest
Hi there,
If any one can help me with this problem I would appreciate it:
"Let O be the circumcenter of Triangle ABC. Suppose AO intersects BD at D and that |AD| = 10, |BD| = 4, and |CD| = 5
Find sin A"
Here is what I have so far:
I draw the triangle inscribed in the circle. Note: A is on Top, B on bottom left, C on botom right, I also assume an acute triangle. Sides a = |BC|, b = |AC| and c = |AB|
Circumradius = R
Using extended law of sines: 2*R = a/Sin(A)
so Sin(A) = a / 2*R and since a = 9, we say Sin(A) = 9 /2R
So I am trying to figure out how to find the circumradius R.
Here are some things I have found from the picture:
2 * angle A = angle BOC by star trek lemma
triangle BOC is isoceles becuase sides |BO| and |CO| = R
Likewise triangles AOB and AOC are isoceles.
We cannot say AD is perpendicular to BC.
I feel like I am very close, but I am missing something very obvious, if anyone can help of give some hints I would be greatly appreciative.
thanks a lot
If any one can help me with this problem I would appreciate it:
"Let O be the circumcenter of Triangle ABC. Suppose AO intersects BD at D and that |AD| = 10, |BD| = 4, and |CD| = 5
Find sin A"
Here is what I have so far:
I draw the triangle inscribed in the circle. Note: A is on Top, B on bottom left, C on botom right, I also assume an acute triangle. Sides a = |BC|, b = |AC| and c = |AB|
Circumradius = R
Using extended law of sines: 2*R = a/Sin(A)
so Sin(A) = a / 2*R and since a = 9, we say Sin(A) = 9 /2R
So I am trying to figure out how to find the circumradius R.
Here are some things I have found from the picture:
2 * angle A = angle BOC by star trek lemma
triangle BOC is isoceles becuase sides |BO| and |CO| = R
Likewise triangles AOB and AOC are isoceles.
We cannot say AD is perpendicular to BC.
I feel like I am very close, but I am missing something very obvious, if anyone can help of give some hints I would be greatly appreciative.
thanks a lot