Question 8 (ii)
In the given figure, O is a point in the interior of a triangle ABC, OD ⊥ BC, OE ⊥ AC and OF ⊥ AB.
Show that (ii) AF2+BD2+CE2=AE2+CD2+BF2
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Solution
(ii) Join OA, OB and OC
We have,OA2+OB2+OC2−OD2−OE2−OF2=AF2+BD2+CE2 AF2+BD2+EC2=(OA2−OE2)+(OC2−OD2)+(OB2−OF2) ∴AF2+BD2+CE2=AE2+CD2+BF2