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Question
If H is the orthocentre of the triangle ABC, then AH is equal to ______.
Options
a cot A
a cot B
b cot A
c cot A
MCQ
Fill in the Blanks
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Solution
If H is the orthocentre of the triangle ABC, then AH is equal to a cot A.
Explanation:
From ΔABH, we have
`(AH)/(sin(90 - A)) = (AB)/(sin(A + B)) = (BH)/(sin(90 - B))`
⇒ AH = `(c cosA)/sinC`
⇒ AH = `(a cos A)/sinA` ∵ `c/sinC = a/sinA`
⇒ AH = a cot A
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Equation of a Straight Line - Equations of Internal and External by Sectors of Angles Between Two Lines Co-ordinate of the Centroid, Orthocentre, and Circumcentre of a Triangle
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