Question

In the given circle , chords AB and CD intersect at O and AO×OB=CO×OD.
Find the x.​ Who gave the right answer I Mark the brainliest answer.

Answer 1

Answer:

Let the length of segment OD be 'x' cm.

⇒ Length of segment CO = CD – OD = (16 – x) cm

According to the intersecting chord theorem, when two chords intersect each other inside a circle, the products of the lengths of their respective segments so formed are equal, i.e.,

When chords AB and CD intersect each other at O, then,

⇒ AO × OB = CO × OD

⇒ 8 × 6 = (16 – x) × x

⇒ 48 = 16x – x2

⇒ x2 – 16x + 48 = 0

⇒ (x – 4)(x – 12) = 0

⇒ x = 4, 12

Since 12 is not in the given options.

∴ Length of segment OD = 4 cm

Step-by-step explanation:

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