# Find the Diameter of the Circle :

AB and CD are two parallel chords of a circle of length 10 cm and 4 cm respectively. If the chords are on the same side of the centre and the distance between then is 3 cm, then the diameter of the circle is

- √21 cm
- √29 cm
- 2√29 cm
- 2√21 cm

**option third is correct.**

**Explanation:-**According to the question,

In right triangle AOF,

AO = (X

^{2}+ 5

^{2})

^{1/2}

CO = {(X + 3)

^{2}+ 2

^{2}}

^{1/2}

AO = CO = radius of the circle

Then, (X^{2} + 5^{2})^{1/2} = {(X + 3)^{2} + 2^{2}}^{1/2}

square on both side,

X^{2} + 5^{2} = (X + 3)^{2} + 2^{2}

X^{2} + 25 = X^{2} + 3^{2} + 2 x 3 x X + 4

25 = 9 + 4 + 6 X

6 X = 25 – 13

6 X = 12

X = 12/6

X = 2 cm

Then, OE = 3 + 2 = 5 cm

In triangle COE,

OC = (5^{2} + 2^{2})^{1/2}

OC = (25 + 4)^{1/2}

OC = (29)^{1/2}

Then, the diameter of the circle = 2 x (29)^{1/2}

= 2(29)^{1/2 }cm

Hence, the answer is (3) 2(29)^{1/2 }cm.