Q. 63.8( 6 Votes )

O is any point ou

Answer :

Given.


OP, OQ and OR are the perpendicular distance of AB, BC and CA respectively from the point O


Formula used.


Area of triangle = × Base × Height



As triangle ABC, triangle OAB, triangle OBC combines to form triangle OAC


Area of triangle ABC = Area of triangle OCB + triangle OAB – triangle OAC


Area of triangle ABC = × Base × Height


× AC × BD


Area of triangle OAC = × Base × Height


× AC × OR


Area of triangle OAB = × Base × Height


× AB × OP


Area of triangle OCB = × Base × Height


× BC × OQ


× AC × BD = ×BC×OQ + ×AB×OP – × AC × OR


As AB = AC = BC (Given)


× AC × BD = × BC×OQ + ×AC×OP – ×AC×OR


Taking common ×AC get removed


BD = OQ + OP – OR


Hence proved;


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