SOLUTION: In triangle ABC, point P is on side BC such that PA = 13, PB = 14, PC = 4, and the circumcircles of triangles APB and APC have the same radius. Find the area of triangle ABC.
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Question 1155795: In triangle ABC, point P is on side BC such that PA = 13, PB = 14, PC = 4, and the circumcircles of triangles APB and APC have the same radius. Find the area of triangle ABC.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
In triangle , point is on side such that
,
,
,
and the circumcircle of triangles and have the same radius. Find the area of triangle .
Note that is a of both circles. Since both circles have the , chord must subtend the angle, i.e. < = < .
Thus, triangle is with .
Let be the of . We see that
so
Then .
Since is also an , we can apply Pythagoras theorem to right triangle to get :
Hence, the area of triangle is:
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