## anonymous one year ago How to find (a) & (b)

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1. anonymous

2. anonymous

|dw:1440494083820:dw|

3. anonymous

In the figure, O is the centre of sector OAD, OC intersects BD at E such that ED=EO and AB = BC find (a) angle AOC, (b) Arc AC:CD

4. anonymous

yeah ...workin it out

5. amilapsn

This would help: |dw:1440496797254:dw|

6. anonymous

got it...are u here?

7. phi

there are probably a few ways. Here is one (not necessarily the best) |dw:1440509331827:dw|

8. phi

angle y plus 2x is 180 (sum of three angles in an isosceles triangle) thus y= 180-2x x+z form a 90 degree angle AOD. so x= 90-z this makes y= 180-2x = 180-180+2z and y= 2z next, we use angle y is the average of the intercepted arcs AC and C' D y= (CF + C'D)/2 arc CF= 1/2 central angle z, so CF= z/2 arc C' D = 90 + z thus we can say $y = \frac{(CF+C'D)}{2} \\ 2z\cdot 2 = CF+C'D \\ 4z = \frac{z}{2} + 90+z$ solve for z, to get z=36 degrees that means arc AC = 36 and arc CD= 90-36= 54 and their ratio is 2/3

9. amilapsn

Another way: |dw:1440564163627:dw|