The angle subtended by a chord at the circumference is $35^\circ$. The angle subtended at the center is:
$70^\circ$
A chord of a circle can subtend an angle at the centre and also an angle at any point on the remaining part of the circumference.
By the central-angle theorem, the angle subtended at the centre is exactly twice the angle subtended at the circumference by the same chord (or arc).
Here the angle at the circumference is \(35^\circ\).
So the angle at the centre \(= 2 \times 35^\circ\).
\(= 70^\circ\).
Key concept: the angle at the centre standing on a given arc is double the inscribed angle standing on the same arc.
Hence the angle subtended at the centre is 70°.
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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?
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