The angle subtended by the diameter at any point on the circle is:
90°
This is the “angle in a semicircle” theorem from circle geometry.
A diameter splits the circle into two equal halves called semicircles, with the diameter as the straight boundary of each.
The theorem states that the angle an arc subtends at the centre is twice the angle it subtends at any point on the remaining circle.
A diameter subtends a straight angle of \(180\degree\) at the centre, so at any point on the circle it subtends \(\dfrac{180\degree}{2} = 90\degree\).
Therefore the angle formed at any point on the circle, with the two ends of the diameter, is always a right angle.
Key concept: any triangle inscribed in a semicircle with the diameter as one side is right-angled at the point on the arc.
Hence the angle subtended by the diameter is 90°.
Similar Questions
A chord AC subtends an angle of 90° at the center O. If the radius of the circle is 8 cm, what is the length of the chord AC?
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Important Questions from Circles, Chords and Tangents
AB is a chord of a circle with centre O and P is any point on the circle. If ∠APB = 112°, then what is the measure of ∠OAB ?
The distance between the centres of two circles is 24 cm. If the radius of the two circles are 4 cm and 8 cm, then what is the sum of the lengths (in cm) of the direct common tangent and the transverse common tangent?
An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. what is ∠BDC equal to?
What can be the maximum number of common tangent which can be drawn to two non-intersecting circles?
There are two identical circles of radius 10 cm each. If the length of the direct common tangent is 26 cm, then what is the length (in cm) of the transverse common tangent?
