Question

AOB is a diameter of a circle. The two chords AC and BD when extended meet at the point E. If <COD=40°, the value of <CED is

(a) 40° (b) 80° (c) 20° (d) 70° ​

Answer 1

Answer:

d)

Step-by-step explanation:

Let AB be the chord of the given circle with centre O and a radius of 10 cm.

Then AB =16 cm and OB = 10 cm

From O, draw OM perpendicular to AB.

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

∴ BM = (162) cm=8 cm

In the right ΔOMB, we have:

OB2 = OM2 + MB2 (Pythagoras theorem)

⇒ 102 = OM2 + 82

⇒ 100 = OM2 + 64

⇒ OM2 = (100 - 64) = 36

⇒ OM=36−−√ cm=6 cm

Hence, the distance of the chord from the centre is 6 cm.