Circle - Formulae & Arcs of Circle

Terms used and Formulas for Circles

If two arcs of a circle (or of congruent circles) are congruent, then corresponding chords are equal.

If two arcs of a circle (or of congruent circles) are congruent, then corresponding chords are equal.

Write the truth value (T/F) of the following with suitable reasons: A circle is a plane figure. Line segment joining the centre to any point on the circle is a radius of the circle. If a circle is divided into three equal arcs each is a major arc. A circle has only finite number of equal chords. A chord of a circle, which is twice as long is its radius is a diameter of the circle. Sector is the region between the chord and its corresponding arc. The degree measure of an arc is the complement of the central angle containing the arc. The degree measure of a semi-circle is 180^0

An arc of length 20pi cm subtends an angle of 144o at the centre of a circle. Find the radius of the circle.

An arc 15 ft long describes an angle of 5 radians at the centre of a circle. Find the radius of the circle.

If two chord of a circle (or of congruent circles) are equal, then their corresponding arcs. (minor, major or semi-circular) are congruent.

i) The radius of a circle is 40cm. Find the angle subtend by an arc of 22 cm at the center of circle in degrees.

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3,4 and 5 units. Then area of the triangleis equal to:

If in the accompanying figure the length of arc AB of circle O is 8pi , what is the number of square units in the area of the shaded region?