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Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of TriangleOrthocentre, pedal triangle basedMedium2 minQB

MathematicsMediumsingle choice

In acute triangle ABC with orthocenter H, let AH=x, BH=y, CH=z. Find $x^{2}$ + $y^{2}$ + $z^{2}$ .

Options:

Answer:

Solution:

AH=2R cos A, BH=2R cos B, CH=2R cos C; since a=2R sin A etc., $\sum x^{2}$ = $4 R^{2}$ $\sum$ (1- $sin^{2}$ A)= $12 R^{2}$ -( $a^{2}$ + $b^{2}$ + $c^{2}$ ).

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Orthocentre, pedal triangle based

⏱ 2mℹ️ Source: QB

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