(A) We know that the diagonals of a parallelogram bisect each other at their point of intersection.Since $O$ is the intersection point,$AC = 2 \times

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(A) We know that the diagonals of a parallelogram bisect each other at their point of intersection.Since $O$ is the intersection point,$AC = 2 \times OA$ and $BD = 2 \times OD$.Given $OA = 3\, cm$ and $OD = 2\, cm$.Therefore,$AC = 2 \times 3\, cm = 6\, cm$.And $BD = 2 \times 2\, cm = 4\, cm$.Hence,the lengths of $AC$ and $BD$ are $6\, cm$ and $4\, cm$ respectively.

Class 9 Mathematics Quadrilaterals Mix Examples - Quadrilaterals

Medium

Diagonals $AC$ and $BD$ of a parallelogram $ABCD$ intersect each other at $O$. If $OA = 3\, cm$ and $OD = 2\, cm$,determine the lengths of $AC$ and $BD$.

A
$AC = 6\, cm, BD = 4\, cm$
B
$AC = 3\, cm, BD = 2\, cm$
C
$AC = 4\, cm, BD = 6\, cm$
D
$AC = 5\, cm, BD = 5\, cm$

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Mix Examples - Quadrilaterals

$D$ and $E$ are the mid-points of the sides $AB$ and $AC$ of $\Delta ABC$ and $O$ is any point on side $BC$. $O$ is joined to $A$. If $P$ and $Q$ are the mid-points of $OB$ and $OC$ respectively,then $DEQP$ is

Medium

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Medium

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$A$ square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

Difficult

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In a parallelogram $ABCD$,$AB = 10 \, cm$ and $AD = 6 \, cm$. The bisector of $\angle A$ meets $DC$ in $E$. $AE$ and $BC$ produced meet at $F$. Find the length of $CF$ (in $cm$).

Difficult

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$D, E$ and $F$ are the mid-points of the sides $BC, CA$ and $AB$ respectively of an equilateral triangle $ABC$. Show that $\triangle DEF$ is also an equilateral triangle.

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Diagonals $AC$ and $BD$ of a parallelogram $ABCD$ intersect each other at $O$. If $OA = 3\, cm$ and $OD = 2\, cm$,determine the lengths of $AC$ and $BD$.

Similar Questions

$D$ and $E$ are the mid-points of the sides $AB$ and $AC$ of $\Delta ABC$ and $O$ is any point on side $BC$. $O$ is joined to $A$. If $P$ and $Q$ are the mid-points of $OB$ and $OC$ respectively,then $DEQP$ is

$ABCD$ is a trapezium such that $AB || CD$. If $\angle A = y + 60^{\circ}$,$\angle B = x + 60^{\circ}$,$\angle C = 3x - 40^{\circ}$ and $\angle D = 3y - 80^{\circ}$,then find the measure of each angle of $ABCD$.

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