Question

In the given figure, ABCD is a rhombus. If OB = 6 units, OC = 8 units and BE = 4 units. Find the length of CE. (CE is perpendicular to AB)

• A. 10 units
• B. √86 units
• C. √84 units
• D. √20.04 units

Answer 1

The correct option is C

√84 units

Since, diagonals of a rhombus intersect at ${90}^{\circ }$,$\Delta BOC$ is a right angled triangle.So, using Pythagoras theorem $O{B}^2$ + $O{C}^2$ = $B{C}^2$
BC = $\sqrt{6^2+8^2}$ = $\sqrt{36+64}$ = $\sqrt{100}$ = 10 units
AE = AB + BE
BE = 4 units
Again applying Pythagoras theorem on $\Delta BEC$
$\sqrt{C{E}^2+B{E}^2}$ = $\sqrt{B{C}^2}$
CE = $\sqrt{B{C}^2-B{E}^2}$ = $\sqrt{{10}^2-4^2}$ = $\sqrt{100-16}$ = $\sqrt{84}$ units