Question

6. The radius of a circle is 17.0 cm and the
length of perpendicular drawn from its centre
to a chord is 80 cm. Calculate the length of
the chord.
​

Answer 1

Answer:

30cm

Step-by-step explanation:

Let O be the center of the circle and AB be the chord. Join OA and OB.

OA = OB = 17cm

OD is perpendicular to AB

OD = 8cm

Therefore, AD = BD        (Since perpendicular from center bisects the chord)

In triangle OAD,

OD² + AD² = OA²

8² + AD² = 17²

64 + AD² = 289

AD² = 289 - 64

AD² = 225

AD = $\sqrt225$

AD = 15cm

Therefore, AD = BD = 15cm

AB = AD + BD = 15 + 15 = 30cm