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Question
In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.
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Solution
Let CD be the median drawn from the vertex C to side AB.
`"BD" = 1/2 × "AB"` ...(D is the midpoint of AB)
∴ BD = `1/2 × 10`
∴ BD = 5 units
In ∆ABC,
seg CD is the median. ...(Given)
By Apollonius theorem,
∴ AC2 + BC2 = 2CD2 + 2BD2
∴ 72 + 92 = 2CD2 + 2(5)2
∴ 49 + 81 = 2CD2 + 2 × 25
∴ 130 = 2CD2 + 50
∴ 2CD2 = 130 − 50
∴ CD2 = `80/2`
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