Home
Class 10
MATHS
In the adjoining firgure O is the centre...

In the adjoining firgure O is the centre of the centre and AB is the diameter. If `angle BCE=20^(@), angle CAE= 25^(@)`, then find the value of `angle AEC`.

Text Solution

Verified by Experts

The angle in circle produced by the chrod CA are `angle AEC and angle ABC`.
`:. angleAEC= angle ABC.......(1)`
Again, the angles in circle produced by the chord BE are `angle BAE and angle BCE`.
`:. angle BAE= angle BCE=20^(@)[ :. angleBCE= 20^(@)]`
Similarly, the angels in circle produced by the chord CE are `angle CBE and angle CAE, :. angle CBE= angle CAE=25^(@) [ :. angleCAE=25^(@)]`
Again, `angle AEB` is a semicircular angle `:. angleAEB=90^(@)`
Then in `Delta ABE, angle ABE=180^(@)-(angle BAE+angleAEB)=180^(@)-(20^(@)+90^(@))=70^(@)`
`:. angle ABC= angleABE- angleBE=70^(@)-25^(@)=45^(@)`
`:.` from (1) we get, `angle AEC= angle ABC=45^(@) :. angleAEC =45^(@)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THEOREMS RELATED TO ANGLES IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE 2.1 (Very Short-Answer Type Questions) MCQs|4 Videos

  • THEOREMS RELATED TO ANGLES IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE 2.1 (True or False)|2 Videos

  • THEOREMS RELATED TO ANGLES IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXAMPLES (Short-Answer Type Questions) MCQs|5 Videos

  • THEOREMS RELATED TO CYCLIC QUADRILATERAL

    CALCUTTA BOOK HOUSE|Exercise Long -answer type questions (L.A.)|12 Videos

  • THEOREMS RELATED TO TANGENT IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE 4.2|23 Videos

Similar Questions

Explore conceptually related problems

In the adjoining figure ,O is the center of the circle and AB is a diameter. If angleAOD=140^(@)andangleCAB=50^(@) , then find value of angleBED

In this figure, O is the centre and AC is the diameter. If angleAOB= 80^@ and angleACE = 10^@ then find the value of angleBED .

Knowledge Check

  • In the adjoining firgure, O is the centre of the circle and AB is its diamter. If AB||CD angle ABC=25^(@) , then the value of angle CED is

    A
    `80^(@)`
    B
    `50^(@)`
    C
    `25^(@)`
    D
    `40^(@)`

  • In the adjoining figure, O is the centre of the circle. If angle AEB=110^(@), angle CBE=30^(@) , then the value of angle ADB is

    A
    `70^(@)`
    B
    `60^(@)`
    C
    `80^(@)`
    D
    `90^(@)`

  • In the adjoining firgure, O is the centre of the circle, if angle BAD=65^(@), angle BDC=45^(@) then the value of angle CBD is

    A
    `65^(@)`
    B
    `45^(@)`
    C
    `40^(@)`
    D
    `20^(@)`

    • Similar Questions

    Explore conceptually related problems

    In the adjoining figure, O is the centre of the circle and AB is one of its diameter . If angleADC = 120^(@) , then the value of angleBAC is

    In the adjoining figure, O is the centre of the circle and AB= AC , if angleABC=32^(@) , then find the value angle BDC

    In the adjoining figure, O is the centre of the circle AC is a diameter and chord DE is parallel to the diameter AC. If angle CBD=60^(@) , find the value of angle CDE

    In the adjoining figure, O is the centre of the circle and AB is a diameter. ABCD IS A CYCLIC QUADRILATERAL . If angleABC=65^(@),angleDAC=40^(@) , then the value of angleBCD is

    In the adjoining figure, O is the centre of circle. If angle BCD=28^(@), angle AEC= 38^(@) , then the value of angle AXB is-

    Home
    Profile