Home
Class 12
MATHS
Two circles of radii 4cm and 1cm touch e...

Two circles of radii 4cm and 1cm touch each other externally and `theta` is the angle contained by their direct common tangents. Find `sin (theta/2)+cos(theta/2) dot`

Text Solution

Verified by Experts

The correct Answer is:
`7//5`
From figure, we have
`sin(theta)/2=3/5`
`cos(theta)/2=4/5`
`:. Sin(theta)/2+cos(theta)/2=7/5`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercises 2.2|8 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise Concept Application Exercises 2.3|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise example|10 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

Two circles of radii 4cm and 1cm touch each other externally and theta is the angle contained by their direct common tangents. Then sintheta is equal to (a) (24)/(25) (b) (12)/(25) (c) 3/4 (d) none of these

Two circles with radii 25 cm and 9 cm touch each other externally. Find the length of the direct common tangent.

Two circles of radii r_(1) and r_(2), r_(1) gt r_(2) ge2 touch each other externally. If theta be the angle between the direct common tangents, then,

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .

Two circles with radii a and b touch each other externally such that theta is the angle between the direct common tangents, (a > bgeq2) . Then prove that theta=2sin^(-1)((a-b)/(a+b)) .

Two fixed circles with radii r_1 and r_2,(r_1> r_2) , respectively, touch each other externally. Then identify the locus of the point of intersection of their direction common tangents.

Two circles touch each other externally. The sum of their areas is 58pi cm^(2) and the distance between their centres is 10 cm. Find the radii of the two circles.

Two circles touch each other externally. The sum of their areas is 74pi cm^(2) and the distance between their centres is 12 cm. Find the diameters of the circle.

If cos2theta=sin4theta , where 2theta and 4theta are acute angles, find the value of theta .

Statement 1 : The number of common tangents to the circles x^(2) +y^(2) -x =0 and x^(2) +y^(2) +x =0 is 3. Statement 2 : If two circles touch each other externally then it has two direct common tangents and one indirect common tangent.