Question

Find AC. With explaination

Answer 1

Answer:

8 cm

Step-by-step explanation:

We have our diagram , As :

Here OC  =  OA  =  OB  =  5  cm  (  Radius )

And

AB  =  BC  =  2√5cm

And OB and AC intersect at " D " .

Here In quadrilateral OABC , OA  =  OC and AB =  BC  , So OABC is a kite and we know in kite diagonals are perpendicular and one diagonal bisect other , So

∠ ADO =  ∠ ADB =  90°∠ ADO =  ∠ ADB =  90°

And

AD  =  CD =  x  

So,

AC  =  AD  +  CD  =  x + x  = 2x  

And Let OD =  y  , So ,  BD  =  5  - y

now we apply Pythagoras theorem in triangle AOD

OD²   +   AD²  = OA² , substitute all the values we get ,

y² + x²  = 5²

y² + x²  = 25

y²  = 25 - x²       --- (1)

we apply Pythagoras theorem in triangle ABD

BD²   +   AD²  = BA² , substitute all the values we get ,

( 5- y )² + x²  = ( 25–√5 )²

25 + y² - 10 y + x²  = 20

y²  = 10y - x² - 5    

Now substitute value from equation ( 1 )

25 - x²   = 10y - x² - 5

10y  = 30

y = 3

hence substitute this value in equation ( 1 ) we get

3² = 25 - x²

x² = 25 - 9

x² = 16

x = 4

AC = 2 ( 4) =  8 cm

Answer 2

Answer:

oc = oa = 2 root5 ( radii.of circle)

angle aoc is 90

so by Pythagoras theorem

ao square + oc square = ac square

ac square =( 2 root 5 )^2 + (2 root 5 )^ 2

ac square = 2* ( 2 root 5 ) ^ 2

ac square = 2* 4 * 5

ac square = 40

ac = root 40

ac = 2 root 10 cm