Home
Class 10
MATHS
AOB is a diamter of a circle. When the ...

AOB is a diamter of a circle. When the chords AC and BD are extended they meet at the point E. if `angle COD=40^(@)`, then the value of `angle CED` is

A

`40^(@)`

B

`80^(@)`

C

`20^(@)`

D

`70^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let us join B,C and C,D AOB is a diameter of the circle with centre at O.
`:. angleACB` is an angle is semicircle.
`:. angle ACB=90^(@).....(1)`
Again `angle BCE=180^(@)-angle ACB=180^(@)-angle 90^(@)` [ from (1)]
`=90^(@).......(2)`
Now, the front central angle produced by the chord CD is `angle COD=40^(@)` and the fron angle is circle is `angle CBD`
by theorem -34 `angle CBD=(1)/(2) angle COD`
or, `angle CBE= (1)/(2) xx 40^(@)=20^(@)....(3) [ :. angle CBD and angle CBE` are same angles]
So from `Delta BCE` we get, `angle BEC+angle BCE+ angle CBE=180^(@)`
`or, angle BEC+90^(@)+20^(@)=180^(@)` [ from (2) and (3)]
or `angle BEC=180^(@)-110^(@)=70^(@)`
`:. angle BEC=70^(@) rArr (d)` is correct.
Promotional Banner

Topper's Solved these Questions

  • THEOREMS RELATED TO ANGLES IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXAMPLES (True or False|2 Videos

  • THEOREMS RELATED TO ANGLES IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXAMPLES (Fill in the blanks)|9 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

The length of tow chords AB and CD of the circle with centre at O are equal . If angle AOB = 60^(@) , then the value of angle COD is .

In the adjoining figure, O is the centre of a circle and AB is one of its diameters. The legth of the chrod CD is equal to the radius of the circle. When AC and BD are extended, they intersect each other at a point P. find the value of angle APB

Chords AC and BD of a circle with centre O interest at right angles at E. If angleOAB =25^@ , then the value of angleEBC is _____

O is the circumecentre of Delta ABC and D is the mid point of BC. If angle BAC=40^(@) , then find the value of angle BOD .

In the figure, O is the centre and BOA is a diameter of the circle. A tangent drawn to the circels at the point P intersects the extended BA at the point T. If angle PBO=30^(@), find the value of angle PAT.

The length of the chords AB and CD of the circle with centre at O equal . If angle AOB = 45^(@) , then angle COD will be.

Manas has drawn a circle with centre O of which AB is a chord. A tangent is drawn at the point B which intersects extended AO at the point. T. If angle BAT=21^(@), find the value of angle BTA.

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 figur, O is the centre of the circle and AB is a diamter. If AB and CD are mutually perpendicualr to each other and angle ADC=50^(@) , then the value of angle CAD

Two circles with centres A and B inrtersect each other at the points C and D. The centre B of the other circle lies on the circle with centre A. if angle CQD=70^(@) , then find the value of angle CPD .