Circles Theorems on Angle Subtended by an Arc of a Circle | CBSE Solutions Class 9 Circles

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Circles Theorems on Angle Subtended by an Arc of a Circle with solved Examples) | CBSESolutions for Class 9 Chapter 10 Circles

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Concept applied in the above problems:Angle Subtended by an Arc of a Circle

CircleTheorems:

CircleTheorems: 1.Congruent arcs ( or equal arcs) of a circle subtend equal angles at the centre.

CircleTheorems: 2.If two chords of a circle are equal, then their corresponding arcs are congruent and conversely, if two arcs are congruent, then their corresponding chords are equal.

CircleTheorems: 3.The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Angles in the same segment of a circle are equal.

CircleTheorems: 4.If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment,the four points lie on a circle (i.e. they are concyclic)

Cyclic Quadrilaterals

CircleTheorems: 5:The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

CircleTheorems: 6:If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.

00:02 CBSE class 9 maths chapter 10 Circles Ex 10.5 Q2. 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 minor arc and also at a point on the major arc.

01:08 Equilateral triangle.

01:58 Angle Subtended by an Arc of a Circle

02:15 Using Theorem:The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

03:09 Cyclic Quadrilaterals

03:25 If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.

04:07 CBSE class 9 maths chapter 10 Circles Ex 10.5 Q3. In Fig. 10.37, ( Angle PQR = 100°, where P, Q and R are points on a circle with centre O. Find (Angle OPR.

06:52 Angle sum property.

07:54 Q4. In Fig. 10.38, ( Angle ABC = 69°, ( Angle ACB = 31° ), find ( Angle BDC).

08:24 Area of triangle.

09:54 CBSE class 9 maths chapter 10 Circles Ex 10.5 Q5. In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ( Angle BEC = 130° and ( Angle ECD = 20°. Find ( Angle BAC.

13:34 Q6. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ( Angle DBC = 70°, ( Angle BAC is 30°, find ( Angle BCD. Further, if AB = BC, find ( Angle ECD..

18:20 CBSE class 9 maths chapter 10 Circles Ex 10.5 Q1. In Fig. 10.36, A,B and C are three points on a circle with centre O such that ( Angle BOC = 30° and ( Angle AOB = 60°. If D is a point on the circle other than the arc ABC, find ( Angle ADC).

19:06 Angles Subtended by an Arc AC of a Circle with centre 'o'.

19:40 Apply circle Theorem:The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

20:42 Q8. If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

21:28 Properties of Parallelogram.

In a parallelogram, pair of opposite sides are parallel and equal.

24:48 Q9. Two circles intersect at two points B and C.Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 10.40). Prove that ( Angle ACP = ( Angle QCD.

25:22 Angles Subtended by an Arc AP of a Circle with centre.

26:36 Aplly Concept of Vertically opposite angles.

27:35 Q10. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

28:35 Triangle Inscribed in a semi circle is Right angles triangle.

29:51 CBSE class 9 maths chapter 10 Circles Ex 10.5 Q11. ABC and ADC are two right triangles with common hypotenuse AC. Prove that ( Angle CAD = ( Angle CBD.

32:20 Apply Concept of Cyclic Quadrilateral.

32:59 Q12. Prove that a cyclic parallelogram is a rectangle.

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CBSE solutions for class 9 maths circles

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NCERT solutions for CBSE class 9 maths circles

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