Question

Two parallel chords which are 10 cm and 24 cm long respectively lie on opposite
sides of center of a circle. The distance between chords is
17 cm. Find the diameter of circle.​

Answer 1

Answer:

diameter

Step-by-step explanation:

here there is a answee

Answer 2

Answer:

Diameter of circle = 26cm

Step-by-step explanation:

Let O is the centre of given circle and r is its radius.

∴ OP ⊥ AB,

OQ ⊥ CD and AB || CD

∴ points P, O, Q are collinear.

Hence, PQ = 17cm

Let, OP= X cm, then

OQ = ( 17 - X) cm

Join OA and OC, then

OA = OC = r

Since, the perpendicular drawn from centre bisects the chords.

∴ AP = PB = 5cm

And CQ = QD = 12 cm

In right angle triangle OAP and OCQ,

OA² = OP ² + AP²

$⇛ {r}^{2} = {x}^{2} + {5}^{2} \: \: \: \: \: \: \: \: \: ....(1) \\ OC²=OQ² + CQ² \\ {r}^{2} = (17 - x {)}^{2} + 1 {2}^{2} \: \: \: \: \: \: \: ....(2)$

∴ form equation (1) and (2),

${x}^{2} + {5}^{2} = (17 - x {)}^{2} + 1 {2}^{2}$

$⇒ {x}^{2} + 25 = 289 + {x}^{2} - 34x + 144$

$⇒34x = 433 - 25$

$⇒34x = 408$

$∴ \: \: \: \: x = \frac{408}{34} = 12cm$

From eqn. (1), r² = x² + 5²

= 12² + 5²

= 144 + 25

= 169

∴ r = 13cm

Hence, diameter of circle 2r = 2⛌13= 26 cm