Question

a circle is passing through three vertices of a rhombus of side 8 cm and its Centre is the fourth vertex of the rhombus. find the length of the longest diagonal of the Rhombus

Answer 1

Answer:

✿Answer:

in the fig 'B' is center

ABCD is rhombus

AD=AB=BC=BD =8cm ( radii)

In rhombus , diagonals are

bisector each other out 90°

BD=BO+OD=4+4=8cm

In Right angle ${∆}^{le}$AOD

↦AD²=AO²+OD²

↦(8²)=AO²+(4)²

↦AO²=64-16=48

↦AO²=$\sqrt{16 \times 3} = 8 \sqrt{3} cm$

ஃ The longest diagonal is $8 \sqrt{3}$