Question

In the given fi gure, AF, CE and BD are diameters intersecting at point O. If AB = CD, then fi nd the measure

of AOB. If the angles subtended by the chords of a circle at the centre are equal, then prove that chords are equal. please​

Answer 1

Answer:

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.

Step-by-step explanation:

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