If `alpha_1 and alpha_2` be the circular measure of the angles subtended by the arcs of lengths `s_1,s_2` at the centres of the circles whose radii are `a_1,a_2` respectively , then show that the angle subtended at the centre by the arc of length `(s_1+s_2)` of a circle whose radius is `1/n(a_1alpha_1+a_2alpha_2)` will be n radians.

If theta_1,theta_2, theta_3 radians be the angles subtended by the arcs of lengths l_1,l_2,l_3 at the centres of the circle whose radii are r_1,r_2,r_3 respectively then show that the angle subtended at the centre by the arc of length (l_1+l_2+l_3) of a circle whose radius is (r_1+r_2+r_3) will be (r_1theta_1+r_2theta_2+r_3theta_3)/(r_1+r_2+r_3) radian.

The length of radius of a circle 14 cm. Determine the circular value of angle subtended by an arc of 11 cm length at the centre of this circle.

If the arcs of the same length in two circles of radii r_1 and r_2 respectively subtend angle pi/3 and 120^@ at the centre ,then the value of (r_1+r_2)/(r_1-r_2) will be

Perimeter of a sector is equal with half of the circumference of a circle. If the angle subtended by the sector at the centre of the circle be n(pi/2-1) , then find the value of n

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use pi = (22)/(7) ).

In a circle, if an arc of 220 cm length subtends and angle of measure 60^@ at the centre, then determine the radius of the circle

In a circle, if an arc of 220 cm length subtends an angle of measure 63^@ at the centre, then determine the radius of the circle.

The condition that the chord xcos alpha +ysin alpha -p=0 of x^2+y^2-a^2=0 may subtend a right angle at the centre of the circle is

Let the sum of n, 2n, 3n terms of an A.P. be S_1, S_2 and S_3 , respectively, show that S_3 =3(S_2-S_1)

If the sums of n, 2n and 3n terms of an A.P. be S_(1), S_(2), S_(3) respectively, then show that, S_(3) = 3(S_(2) - S_(1)) .