Question

Fill In The Blanks

AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30cm, then the distance of AB from the centre of the circle is ________.

Answer 1

Given:
AD is a diameter
AB is chord
AD = 34 cm
AB = 30 cm


Let O be the centre of the circle.
AO = OD = 17 cm ...(1)

Let OL is a line perpendicular to AB, where L is the point on AB.
Then, AL = LB = 15 cm ...(2) (∵ a perpendicular from the centre of the circle to the chord, bisects the chord)

In ∆ALO,
Using pythagoras theorem,
AL² + LO² = AO²
⇒ 15² + LO² = 17² (From (1) and (2))
⇒ 225 + LO² = 289
⇒ LO² = 289 − 225
⇒ LO² = 64
⇒ LO = 8 cm

Thus, the distance of the chord from the centre is 8 cm.


Hence, the distance of AB from the centre of the circle is 8 cm.