Question

Assertion: ABCDE is a regular pentagon inscribed in a circle with centre O. ∠OCE = 18°.

Reason: Equal chords make equal angles at the centre.

पर्याय

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true but R is the incorrect reason for A.

Explanation:

In a regular pentagon ABCDE inscribed in a circle with center O, all sides (chords) are equal. Since the pentagon is regular, each side subtends the same angle at the center O.

Therefore, ∠OCE = 18° is correct as each central angle corresponding to a side of a regular pentagon measures `"360°"/5` = 72°. 

Also, from point C, the angle to E subtends half of the central angle, giving 18°.

Equal chords in a circle subtend equal angles at the center. This explains why the angles related to these equal chords (sides of the pentagon) are equal.