Home
Class 12
MATHS
A circle centred at 'O' has radius 1 and...

A circle centred at 'O' has radius 1 and contains the point A. Segment AB is tangent to the circle at A and `angleAOB =theta`. If point C lies on OA and BC bisects the angle ABO then OC equals

A

`sectheta(sectheta-tantheta)`

B

`(cos^2theta)/(1+sintheta)`

C

`1/(1+sintheta)`

D

`(1-sintheta)/cos^2theta`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Using property of angle bisector, we get
`(OB)/(AB)=(OC)/(AC)rArr sectheta/tantheta=x/(1-x)`
`or x=sectheta/(sectheta+tantheta)`
`xsectheta(sectheta-tantheta)=1/(1+sintheta)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Matrix)|3 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Single)|57 Videos

  • TRIGONOMETRIC EQUATIONS

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

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

A circle centred at O has radius 1 and contains the point A. Segment AB is tangent to the circle at A and angle AOB=theta If point C lies on AA and BC bisects the angle ABO then OC equals

A circle centred at O has radius 1 and contains the point A. Segment AB is tangent to the circle at A and angle AOB=theta If point C lies on AA and BC bisects the angle ABO then OC equals

A circle centred at 'O' has radius 1 and contains the point A .Segment AB is tangent to the circle at A and /_AOB=theta. If point C lies on OA and BC bisects the angle ABO then OC equals

In figure PQ is tangent to the circle with centre at O at the point B , if angle AOB = 100^(@) , then angle ABP is equal to

In figure-3, PQ is tangent to the circle with centre at O, at the point B. if angleAOB=100^(@) , then angleABP is equal to

In the given, figure , O is the centre of the circle and AD is a tangent to the circle at.A if angle CAD =55^@ and angle ADC=25^@ , then find angle ABO .

PA and PB are two tangents to a circle with centre O, from a point P outside the circle . A and B are point P outside the circle . A and B are point on the circle . If angle PAB = 47^(@) , then angle OAB is equal to :

In the figure, O is the centre of a circle and AT is a tangent at point A. The measure of angle BAT is:

The congruent circles with centres Oand O' intersect at two points A and B. Then, angleAOB=angleAO'B .