Angle Subtended by the Diameter to any Point on the Circle is equal to 90 degrees
A triangle ha...
Question
A triangle has a side as diameter of a circle, and three of its vertices lie on the circle. What type of triangle is this?
A
Acute triangle
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B
Right triangle
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C
Obtuse triangle
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Solution
The correct option is B Right triangle The angle subtended by the aiameter to any point on the circle is equal to 90o.
We know that the angle subtended by an arc at the centre of a cirlce is double the angle subtended by the arc at any point on the circle.
Here, the angle subtended by the arc AB at the centre is 180o.
∴∠ACB=180o2=90o
A right triangle is a triangle whose one of the angles is 90o. ∴△ABC is a right triangle.
Whereas, an acute triangle has all the angles as acute.
Hence, it is not an acute triangle.