A chord of length 24 cm subtends a right angle at the center of the circle. What is the radius of the circle?
\(12\sqrt{2}\) cm
The two radii to the ends of the chord and the chord form a triangle with a right angle at the centre.
By Pythagoras: \(r^2 + r^2 = 24^2 \Rightarrow 2r^2 = 576 \Rightarrow r^2 = 288\).
\(r = \sqrt{288} = 12\sqrt{2}\) cm (equivalently, chord \(= r\sqrt{2}\)).
Hence, the radius of the circle is \(12\sqrt{2}\) cm.
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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 ?
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?
AB is a chord in the minor segment of a circle with centre O. C is a point on the minor arc (between A and B). The tangents to the circle at A and B meet at a point P. If ∠ACB = 108°, then ∠APB is equal to:
