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| 1. |
Teurom 10.8 circle in class 9 |
| Answer» Draw a circle and and take two points and name it A and B. Let the centre of the the circle be O. Join OA and OB. mark a point P on the other side of the circle. Now join AP and BP. Join OP and extend to the other side say PQ. PROOF:consider triangle AOPsince OP=OA (radii)The triangle is isosceles. So,Angle OPA = OAPlet the equal angles be \'x\'.. ....(1)Similarly, Angle OAP=OBPlet the equal angles be \'y\'... ......(2)From (1and2)Angle APB = x+y........(3)Angle AOQ = x+x=2x(exterior angle property)Angle BOQ = y+y=2y(exterior angle property)Angle AOB = AOQ+BOQAOB = 2x+2y = 2(x+y)Therefore angle AOB = 2*ABP( from (3)). | |