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Home /Doubts and Solutions/CBSE/Class 9/Mathematics/Circles/Angle Subtended By The Chord

# Angle Subtended By The Chord Free Doubts and Solutions

## Find value of x if o is center

Asked by yogeshthakur3300 28th December 2018, 8:24 AM
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## Prove that the circle drawn on any equal side of an isosceles triangle as an diameter bisects the third side .

Asked by Vikas 12th January 2018, 10:54 AM
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## Please solve question no 12 with proper explanation

Asked by adityaahuja099 2nd December 2017, 10:05 AM
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## Please solve question no 8 with proper explanation

Asked by adityaahuja099 28th November 2017, 5:41 PM
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## Please solve question no 5 with proper explanation

Asked by adityaahuja099 26th November 2017, 3:41 PM
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## Please solve question no 4 with proper explanation

Asked by adityaahuja099 26th November 2017, 3:37 PM
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## Please solve question no 1 with proper explanation

Asked by adityaahuja099 26th November 2017, 3:35 PM
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## Please solve question no 10 with proper explanation

Asked by adityaahuja099 20th November 2017, 7:57 PM
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## Please solve question no 7 with proper explanation

Asked by adityaahuja099 20th November 2017, 7:50 PM
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## Please solve question no 6 with proper explanation

Asked by adityaahuja099 20th November 2017, 7:48 PM
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## In the given figure if ABCD is a rhombus diagonals AC and BD intersect at o   and he is a point lying on the circle with Centre o then the sum of the measures of angle BAE and angle EDC is??

Asked by shriya.pandey182 20th October 2017, 11:01 PM
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## How to prove that angle subtended by the chord are equal to the chords?

Asked by Preeti 11th March 2017, 7:38 PM
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## A circle has radius root 2 cm. it is diveded into two segments by a chord of length 2 cm.prove that the angle subtended by thechord at a point in major segment is 45 degree.

Asked by Snehal Ambekar 12th March 2016, 6:30 PM
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## Prove that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Asked by mkmishra101 3rd March 2016, 5:38 PM
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## I didn't understood the sentence " The degree measure of a minor arc is the measure of the central angle subtended by the arc." Please help me with a diagram.

Asked by parthapratimdeori1998 17th February 2016, 11:08 AM
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## please ignore tech team testing

Asked by Srinivas 3rd September 2015, 3:44 PM
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## qus 1 -Prove that if the bisector of any angle of a triangle and the perpendicular bisector of its opposite side intersect, the will intersect on the circumcircle of the triangle.   qus 2 - what is circumcircle?

Asked by Varsha 25th January 2015, 6:36 PM
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## <div>In the followin figure, A is the centre of the circle. ABCD isa paralleolgram and CDE is a straight line. Find <img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=10760cd90092037cd4f09dde6a7d7bb7.png" alt="angle" align="middle" />BCD:<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=10760cd90092037cd4f09dde6a7d7bb7.png" alt="angle" align="middle" />ABE</div> <div><img src="data:image/png;base64,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" alt="" /></div>

Asked by kumar.ashlesha 16th January 2015, 10:24 PM
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## Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B. Prove that QA=QB.

Asked by ishansaini243 11th January 2015, 3:23 PM
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## In the figure, two circles intersect at B and C. Through B two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively. Prove that ACP = DCQ.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the given figure, O is the centre of the circle. If OAC = 35o and OBC = 40o, find the value of x.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## Prove that the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## O is the circumcentre of the ABC and D is the mid point of the base BC. Prove that BOD = A.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In figure, O is the centre of circle. Calculate APC and AOC.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In circle having centre 'O' find BAC

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the figure, O is the centre of the circle and BAC = 60o. Find the value of x.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the figure, PQ is a diameter of the circle and XY is chord equal to the radius of the circle. PX and QY when extended intersect at point E. Prove that PEQ = 60o

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the figure, ABC = 45o, Prove that OA OC.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the figure, chord AB of circle with centre O, is produced to C such that BC = OB. CO is joined and produced to meet the circle in D. If ACD = y and AOD = x, show that x = 3y.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## Two circles intersect at two points A and B. AD and AC respectively are diameters to the two circles. Prove that B lies on the line segment DC.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the given figure, AB is a side of a regular hexagon and AC is a side of a regular octagon inscribed in a circle with centre O. Calculate angles AOB and AOC.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the given figure BD is the side of a regular hexagon, DC is a side of a regular pentagon and AD is a diameter. Calculate:

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the given figure, AB = BC = CD and angle ABC is 132o. Calculate angle COD.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the figure, O is the centre of the circle and the length of the chord AB is twice the length of chord BC. If angle AOB = 108o, find angle BOC.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## The given figure shows a circle with centre O. Also PQ = QR = RS and angle PTS = 75o. Calculate: .

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## In the given diagram, chord AB = Chord BC. What is the relation between angle AOB and angle BOC?

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## A regular polygon is inscribed in a circle. If a side subtends an angle of 36o at the centre, find the number of sides of the polygon. Name the polygon.

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## A regular pentagon is inscribed in a circle. What angle does each side subtend at the centre?

Asked by Topperlearning User 4th June 2014, 1:23 PM
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## Prove that equal chords of congruent circles subtend equal angles at their centres

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## Prove that equal chords of a circle subtend equal angles at the centre.

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