The radius of a circle is 13 cm and the length of one of its chords is 10 cm. What is the distance of the chord from the centre?
12 cm
The perpendicular drawn from the centre of a circle to a chord bisects the chord.
So half of the chord length = 10/2 = 5 cm.
Let d be the distance of the chord from the centre. Using the Pythagorean theorem in the right triangle formed by the radius, half-chord and the perpendicular distance: d^2 + 5^2 = 13^2.
d^2 = 169 - 25 = 144, so d = 12 cm.
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:
