Mathematics - Properties of Triangle Question with Solution | TestHub

MathematicsProperties of TriangleLength of angle bisector and median / Dist. between sp. PointsMedium2 minQB

MathematicsMediumsingle choice

In triangle ABC, medians AD and CE meet at centroid G. If AD=5, $∠ D A C$ = $π$ /8 and $∠ A CE$ = $π$ /4, find area $Δ A BC$ .

Options:

Answer:

Solution:

The centroid has AG=2AD/3=10/3. In triangle AGC, $∠ G A C$ = $π$ /8 and $∠ A CG$ = $π$ /4, so GC=AG sin( $π$ /8)/sin( $π$ /4). As $∠ A GC$ =5 $π$ /8, $Δ A BC$ =3 $Δ A GC$ =3·AG·GC·sin(5 $π$ /8)/2. Use sin(5 $π$ /8)=cos( $π$ /8) to simplify to (50/3)[sin( $π$ /8)cos( $π$ /8)/sin( $π$ /4)]=(25/3).

Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Length of angle bisector and median / Dist. between sp. Points

⏱ 2mℹ️ Source: QB

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