Write True/False for each and write the reason also for your answer.

(i) The angles subtended at any two points lying of the circle by every chord are equal.

(ii) In figure, AB is a diameter of a circle and C is any point on the circle. Then AC² + BC² = AB².

(iii) In figure 12.48, if ∠ADE = 120°, then ∠EAB = 30°.

(iv) In figure 12.48, ∠CAD = ∠CED.

(i) False

We know that if two points lie on the same segment, then they are equal.

Hence, it is false.

(ii) False

⇒ ∠C = 90°

∴ By Pythagoras Theorem,

⇒ AB² = AC² + BC²

(iii) True

Join AD, DE, EB and DB.

∠ADB = 90°

And ∠BDE = 120° - 90° = 30°

We know that angles that lie on the same segment are equal.

∴ ∠BDE = ∠EAB = 30°

(iv) True

Join AC, CE, CD, DE, AE and AD.

ACDE is minor segment of the circle.

We know that angles in the same segment are equal.

∴ ∠CAD = ∠CED