in the figure O is the centre of the circle radius is 3cm angle AOB = 60 degree. find perimeter of triangle AOB
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Iam 8 th std student
Answers
Step-by-step explanation:
To find the perimeter of triangle AOB, we need to find the length of each of its sides.
First, we can use the fact that angle AOB is 60 degrees to find the measure of angle AOC, which is 180 - 60 - 90 = 30 degrees. Since O is the center of the circle and AC is a radius, this means that angle AOC is also a 30-degree central angle.
Since the radius of the circle is 3 cm, we can use the formula for the length of an arc to find the length of arc AC:
arc AC = (30/360) * 2 * pi * 3 cm
= pi cm
Since AC is a radius and a diameter of the circle is a straight line, we know that AC is also a diameter of the circle. The diameter of the circle is 2 * 3 cm = 6 cm, so AC is also 6 cm.
Now, we can use the Pythagorean Theorem to find the length of side AO:
AO^2 = AC^2 - OC^2
= 6^2 - 3^2
= 9
AO = sqrt(9)
= 3 cm
Similarly, we can find the length of side BO:
BO^2 = AC^2 - OB^2
= 6^2 - 3^2
= 9
BO = sqrt(9)
= 3 cm
Finally, we can add up the lengths of the sides to find the perimeter of the triangle:
Perimeter = AO + BO + AC
= 3 cm + 3 cm + 6 cm
= 12 cm
Therefore, the perimeter of triangle AOB is 12 cm.