Home
Class 10
MATHS
‘O’ is any point in the interior of a tr...

‘O’ is any point in the interior of a triangle ABC. If ` OD bot BC, OE bot`AC and OF `bot` AB, show that
(i) `OA^(2) + OB^(2) + OC^(2) - OD^(2) - OE^(2) - OF^(2) = AF^(2) + BD^(2) + CE^(2)`
(ii) `AF^(2) + BD^(2) + CE^(2) = AE^(2) + CD^(2) + BE^(2)`.

Promotional Banner

Topper's Solved these Questions

  • SIMILAR TRIANGLES

    NCERT GUJARATI|Exercise OPTIONAL EXERCISE|6 Videos

  • SIMILAR TRIANGLES

    NCERT GUJARATI|Exercise TRY THIS|6 Videos

  • SIMILAR TRIANGLES

    NCERT GUJARATI|Exercise EXERCISE - 8.3|6 Videos

  • SETS

    NCERT GUJARATI|Exercise Try This|11 Videos

  • STATISTICS

    NCERT GUJARATI|Exercise THINK AND DISCUSS|8 Videos

Similar Questions

Explore conceptually related problems

In the given figure, O is a point in the interior of a DeltaABC, OD bot BC, OE bot AC" and "OF bot AB . Show that : OA^(2)+OB^(2)+OC^(2)-OD^(2)-OE^(2)-OF^(2)= AF^(2)+BD^(2)+CE^(2) .

In the given figure, O is a point in the interior of a DeltaABC, OD bot BC, OE bot AC" and "OF bot AB . Show that : AF^(2)+BD^(2)+CE^(2)=AE^(2)+CD^(2)+BF^(2) .

ABCD is a rhombus. Prove that AB^(2)+BC^(2)+CD^(2)+DA^(2)= AC^(2)+BD^(2) .

D is a point on the side BC of a triangle ABC such that /_ADC= /_BAC . Show that CA^(2)= CB*CD .

ABD is a triangle right angled at A and AC bot BD Show that (i) AB^(2) = BC .BD. (ii) AC^(2) = BC.DC (iii) AD^(2) = BD .CD.

In the given figure, AD is a median of a DeltaABC and AM bot BC . Prove that : AC^(2)+AB^(2)= 2AD^(2)+(1)/(2) BC^(2)

ABC is a right triangle right angled at B. Let D and E be any points on AB and BC respectively. Prove that AE^(2) + CD^(2) = AC^(2) + DE^(2) .

In the given figure, D is a point on hypotenuse AC of triangleABC , such that BD bot AC, DM bot BC" and "DN bot AB . Prove that : DN^(2)= DM*AN

In the given figure, ABD is a triangle right angled at A and AC bot BD . Show that AD^(2)= BD*CD