Line Perpendicular to a Chord from the Center of the Circle
The base QY o...
Question
The base QY of the given triangle is half of the chord ZY. Also, one of the sides of the triangle passes through the center of the circle. Comment on the type of the triangle.
A
Acute triangle
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B
Right triangle
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C
Obtuse triangle
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D
Scalene triangle
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Solution
The correct option is D Scalene triangle Given: QY=ZQ ∴Q is the midpoint of the chord ZY.
Also, QX passes through the center of the triangle. ∴QX must be perpendicular to ZY. ⇒∠XQY=90o
Hence, the given triangle is a right triangle.
Also, the length of ZY is less than the diameter of the circle. ∴QY is less than the radius of the circle.
However, the side QX passes through the center and touches the circle. ∴QX is more than the radius of the circle.
Hence, QX and QY are of different lengths.
We know that hypotenuse of a right triangle is the largest side. ∴ All the sides are of different lengths, which is a property of a scalene triangle.