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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