Home
Class 12
MATHS
If theta1,theta2, theta3 radians be the ...

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.

Text Solution

Verified by Experts

The correct Answer is:
Then `theta=(l_1+l_2+l_3)/(r_1+r_2+r_3)= (r_1theta_1+r_2theta_2+r_3theta_3)/(r_1+r_2+r_3)` radian
Promotional Banner

Topper's Solved these Questions

  • MEASURMENT OF TRIGONOMETRICAL ANGLES

    CHHAYA PUBLICATION|Exercise EXERCISE 1|50 Videos

  • MEASURMENT OF TRIGONOMETRICAL ANGLES

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Multiple correct Answers Type )|5 Videos

  • MEASURES OF DISPERSION

    CHHAYA PUBLICATION|Exercise Sample question for competitive exams (D. Assertion-Reason Type)|2 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

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

If r_1 =r_2+r_3+r, prove that the triangle is right angled.

The ex-radii r_1,r_2,r_3 or Delta ABC are in H.P. Show that its sides a,b,c are in A.P.

If in a triangle (1-r_1/r_2)(1-r_1/r_3)=2, then the triangle is

Find the equation of the curve whose parametric equations are x=1+4costheta,y=2+3sintheta,theta in R .

If r/(r_1)=(r_2)/(r_3), then

If the arc of a circle of radius 60 cm subtends and angle 2/3 radian at its centre , then the length of the arc will be

In a simple, body-centred and face-centred cubic unit cell, the radii of constituent particles are r_(1),r_(2)andr_(3) , respectively. If the edge length of each type of these unit cells be a, then find the ratio of r_(1),r_(2)andr_(3) .

If I is the incenter of Delta ABC and R_(1), R_(2), and R_(3) are, respectively, the radii of the circumcircle of the triangle IBC, ICA, and IAB, then prove that R_(1) R_(2) R_(3) = 2r R^(2)