In a triangle ABC, AB = 16, AC = 9. Find the length of the altitude to BC if the circumradius is 9.
Answer: 8
Explanation:
Consider the figure below.
We know that,
Area of a triangle = abc/4R where a,b,c are the sides of the triangle and R is the circumradius.
Hence,
Area of a triangle = abc/4R where a,b,c are the sides of the triangle and R is the circumradius.
Hence,
(AB x BC x AC)/4R = (1/2) x BC x AD
(16 x BC x 9)/36 = (1/2) x BC x AD
Therefore, AD = 8.
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