Question

ABCD is a rhombus where angle ADC=120°. There are two fire stations at C and
D and fire is reported at O. Which fire station team can reach early and why ?​

Answer 1

Answer:

I suppose point O is the intersection of diagonals of rhombus ABCD.

Then the answer is D fire station team.

Explanation:

Diagonals of rhombus are perpendicular to each other, (property of rhombus)

means angle DOC=90° (draw figure you'll get it)

Diagonals of rhombus are angle bisectors of the opposite angles, (property of rhombus)

means angle ODC=60° (1/2 of 120°) and angle OCD=30° (half of 60°)

{you must know why OCD is 30 as sum of all angles of quadrilatral is 360 and opp. sides of rhombus are equal}

now in triang. DOC angle DOC =90°

By 30-60-90 theorem ,

if seg OD =x, then seg OC= x√3

as d(OD) is less than OC, fire station team D will come fast.