Question

Chords AB and CD intersect at the
point O. AB = 40 cm, OB = x cm,
CO = 15 cm, DO = 20 cm. Find the
possible values of x.
​

Answer 1

Solution :

Chords AB and CD intersect at point O.

Given

• AB = 40 cm
• OB = x cm
• CO = 15 cm
• DO = 20 cm

Now, before solving it. We have to learn a theorem

Intersecting chord theorem : When two chords intersect each other inside a circle, the product of their segments are equal.

Therefore,

Product of AO and OB = Product of CO and DO

⇒ AO * OB = CO * DO

From figure,

⇒ (AB - OB) * OB = CO * DO

Substituting the given values

⇒ (40 - x) * x = 15 * 20

⇒ 40x - x² = 300

⇒ 0 = x² - 40x + 300

⇒ x² - 40x + 300 = 0

Splitting the middle term

⇒ x² - 10x - 30x + 300 = 0

⇒ x(x - 10) - 30(x - 10) = 0

⇒ (x - 30)(x - 10) = 0

⇒ x - 30 = 0 or x - 10 = 0

⇒ x = 30 or x = 10

Hence, the possible values of x are 30 cm or 10 cm.