Home
Class 10
MATHS
In the adjoining figure, two circles wit...

In the adjoining figure, two circles with centres P and Q intersect each other at the points B and C, ACD is a line segment . If `angleARS=150^(@)andangleBQC=x^(@)` , then find the value of x.

Text Solution

Verified by Experts

ARBC is a cyclic quadrilateral,
`thereforeangleARB+angleACB=180^(@)`
or,` 150^(@)+angleACB=180^(@)`
or, `angleACB=180^(@)-150^(@)=30^(@)`
Again , `angleACD=angleACB+angleBCD=1 " straight angle" = 180^(@)`
or, `30^(@)+angleBCD=180^(@)"or"angleBCD=180^(@)-30^(@)=150^(@)`
Now , in the circle with center Q, ` angle BCD` is an angles in circle and reflex `angleBQD` is its central angle both produced by the circular are `overset(frown)(BD)` .
`therefore" reflex " angleBQD=2angleBCD`
or `360^(@)-angleBQD=2angleBCD" or ",360^(@)-x^(@)=2xx150^(@)" or ",x^(@)=360^(@)-300^(@)" or " ,x^(@)=60^(@)`
Hence the value of x is 60.
Promotional Banner

Topper's Solved these Questions

  • THEOREMS RELATED TO CYCLIC QUADRILATERAL

    CALCUTTA BOOK HOUSE|Exercise Example (Long-answer type questions)|20 Videos

  • THEOREMS RELATED TO CYCLIC QUADRILATERAL

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-3(Very short - answer type questions)(MCQ)|4 Videos

  • THEOREMS RELATED TO CYCLIC QUADRILATERAL

    CALCUTTA BOOK HOUSE|Exercise Fill in the blanks:|6 Videos

  • THEOREMS RELATED TO CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 1 (Long - answer type question )|9 Videos

  • THEOREMS RELATED TO ANGLES IN A CIRCLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE 2.3 (Long Answer Type Questions)|14 Videos

Similar Questions

Explore conceptually related problems

In the adjoining figure , the diagonals of the cyxlic quadrilateral PQRS intersect each other at the point X in such a way that anglePRS=65^(@) andangleROS=45^(@) . Find the values of angleSQP and angleRSP .

In the adjoining figure , two circles intersect each other at the points P and Q. If angleQAD=80^(@)andanglePDA=84^(@) , then find the value of angleQBCandangleBCP

Like the adjoining figure, draw two circles with centres C and D which intersect each other at the points A and B . Draw a straight line through A which intersects the circle C at the point P and the circle with centre D at the point Q. Prove that (i) angle PBQ= angle CAD (ii) angle BPC= angle BQD .

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 .

Find the area of the shaded region in the figure, in which two circles with centres A and B touch each other at the point C, where AC=8cm and AB=3cm

The line segments AB and PQ intersect each other at the point C . AP and BQ are perpendiculars on AB respectively. If CA=20cm , CB=8cm and AP=10cm , then find the value of BQ .

Two chords AB and CD of a circle with centre O intersect each other at the point P. If ∠AOD =20° and ∠BOC = 30°, then ∠BPC is equal to?

Two tangents drawn at the point A and B on a circle intersect each other at the point P. If angle APB=60^(@), then anglePAB=

If two chords AB and CD of a circle with centre O, when produce intersect each other at the point P, then prove angleAOC-angleBOD = 2angleBPC .

The two circles with centre X and Y intersect each other at the points A and B, A joined with the mid -point S of XY and the perpendicular on SA through the point A is drawn which intersect the two circles at the point P and Q .Prove that PA = AQ.