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
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Important Questions from Circles, Chords and Tangents
A chord 21 cm long is drawn in a circle of diameter 25 cm. The perpendicular distance of the chord from the centre is:
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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?
In a circle with centre O, an arc ABC subtends an angle of 132° at the center of the circle. Chord AB is produced to point P. Then ∠CBP is equal to∶
