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Grade 99 grade maths

In a Triangle ABC, angle A = 900 , CA=AB,
D is a point on BC produced. Prove that AD2=AC2+BD X CD

Profile image of Dipankar Ghosh
11 Years agoGrade 9
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1 Answer

Profile image of Sumit Majumdar
11 Years ago
68-2201_1.jpg
From the figure, we see that:
AD^2=AE^2+ED^2=\left(AC+CE \right )^2+ED^2=AC^2+CE^2+AC\cdot CE+ED^2
From symmetry of triangles, we know that
AC\cdot CE=BC\cdot CD
So, we get
AD^2=AC^2+CE^2+BC\cdot CD+ED^2=AC^2+BC\cdot CD+CD^2=AC^2+BC\left(BC+CD \right )=AC^2+BD\cdot CD

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