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;

Rate this question :

In triangle ABC <West Bengal Mathematics

In triangle ABC oWest Bengal Mathematics

AD and BE are theWest Bengal Mathematics

D is the midpointWest Bengal Mathematics

AD is the median West Bengal Mathematics

D is the midpointWest Bengal Mathematics

D, E and F are miWest Bengal Mathematics

A line parallel tWest Bengal Mathematics

D is the midpointWest Bengal Mathematics

O is any point ouWest Bengal Mathematics