Question

Fill In The Blanks

AD is a diameter, ,of circle and AB is chord. If AD = 34 cm, AB = 30 cm, then BD = ____________

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

Now, In ∆ABD,
Using mid-point theorem: The line segment joining the mid-points of two sides of a triangle is parallel to the third side and is equal to the half of it.
Therefore, LO = $\frac{1}{2}$BD
⇒ BD = 2LO
⇒ BD = 2(8)
⇒ BD = 16 cm​


Hence, BD = 16 cm.