A square has two of its vertices on a circle
and the other two on the tangent to the circle,
If the diameter of the circle is 10, determine
the side of the square.
Answers
8 cm would be the side of the square.
Step-by-step explanation:
Given that,
The diameter of the circle = 10 cm
which has two vertices of the square on it and the two other sides on its tangent.
Considering O be the center of the circle and ABCD to be square with B as its midpoint on AC. So, construct the ΔOAC with O meeting B.
Now,
OA = OC = OD = 10/2 = 5cm (∵ all are the radii of the circle)
Now,
Let x be the side of the square. So,
OB = x - 5
Since AB = x/2, we can use the Pythagoras theorem:
So,
AB^2 + OB^2 = OA^2
⇒ (x/2)^2 + (x-5)^2 = 5^2
⇒ (1/4)x^2 + x^2 - 10x + 25 = 25
⇒ (5/4)x^2 - 10 x = 0
⇒ x(5/4x - 10) = 0
∵ x = 0 0r x = 8
Since 0 cannot be possible, x = 8 cm.
Thus, each side of the square measures 8cm.
Learn more: find the side of the square
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