16. ABCD is a square. ABO is an equilateral triangle
inside the square. Find ZDOC.
Answers
Answer:
2×75.=150'
Step-by-step explanation:
A square ABCD has an equilateral triangle AOB inscribed in it. What is the value of the angle COD?
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3 Answers

Ved Prakash Sharma, former Lecturer at Sbm Inter College, Rishikesh (1971-2007)
Answered 2 years ago · Author has 9.3K answers and 5.1M answer views
ABCD is a square and an equilateral triangke AOB inscribed in it. let each side of square is
2a unit. The mid points of AB is M and mid
Point of CD is N .join M to N, O will lie on MN.
In right angled triangle OMA
OM/AM=tan60°
OM/a =3^1/2 , or OM =a.3^1/2
ON =MN -OM =2a- a.3^1/2=(2–3^1/2).a.
In right angled triangle DNO
tan DON =DN/ON =a/(2–3^1/2).a
= { 1/(2–3^1/2)}×{(2+3^1/2)/(2+3^1/2)}
=(2+3^1/2)/(4–3) =(2+3^1/2) =tan 75°
or Angle DON =75°
Angle COD = 2×Angle DON
= 2 × 75° = 150° , Answer.
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