Cyclic quadrilaterals

Mathematics for class 9

1. Cyclic Quadrilaterals

2. LOOK AT THE VIDEO 1.Define Quadrilateral. 2.What are the types of Quadrilateral? 3.Identify the Quadrilateral. 4.Draw a circle and mark the parts of the circle. 5.What do you mean by exterior angle? 6.Is trapezium is a Quadrilateral?

3. Cyclic Quadrilaterals

4. STATEMENT A cyclic quadrilateral is a quadrilateral which has all it’s four vertices lying on a circle.

5. Opposite angles of a cyclic quadrilateral are supplementary . Theorem Now let’s see this video 5

6. Problem If PQRS is a cyclic quadrilateral in which ∠PSR=70° and ∠QPR=40°, then find ∠PRQ 6 6

7. PQRS is a cyclic quadrilateral Given ∠PSR =70° ∠PSR+∠PQR=180° 70°+∠PQR=180° ∠PQR=110° In DPQR we have,   ∠PQR+∠PRQ+∠QPR =180°  110°+∠ PRQ +40°=180°   ∠PRQ =30°     Solution 7

8. EXTERIOR ANGLE OF CYCLIC QUADRILATERAL 8

9. An exterior angle of a quadrilateral is an angle in its exterior formed by one of its sides and the extension of an adjacent side.

10. OBSERVE THE VIDEO https://youtu.be/O9DZyZMG4Eo

11. THEOREM 11 If one side of a cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.

12. LET’S SEE

13. In the figure given, find the value of x° and y°. Solution: By the exterior angle property of a Cyclic quadrilateral, we get, y°=100° and x°+30°=60° and so x° = 30°

14. RECAP 1.If a pair of opposite angles of a quadrilateral supplementary then quadrilateral_____ 2. As the length of the chord decreases, the distance from the centre______ 3.state exterior angle of a cyclic quadrilateral. 4. Sum of opposite angles of a cyclic quadrilateral is_____

15. QUIZZ....... https://quizizz.com/admin/quiz/5d9dc2b290d89e001b48c867/cyclic-quadrilaterals

16. ASSIGNMENT

17. 2. .In the given figure, AC is the diameter of the circle with centre O. If <ADE = 30° ; <DAC = 35° and <CAB = 40°. Find ( i ) <ACD   (ii)  <ACB  (iii)  <DAE 1.Find the value of x in the given figure.  3. Find all the angles of the given cyclic quadrilateral ABCD in the figure 4.

18. https://sweetly25.blogspot.com/2022/11/assignment-cyclic-quadrilateral.html BLOG