Find AC. With explaination

Answers
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:
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