A chord subtends an angle 80° at the centre of a circle. What is the angle subtended by the chord in the minor segment of the circle?

Question

A chord subtends an angle 80° at the centre of a circle. What is the angle subtended by the chord in the minor segment of the circle? (A) 140° (B) 145° (C) 70° (D) 110°

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/94c2c576fbece1c7c6505d33337b0dae-.png" /> angle ACB =80° Reflex angle ACB =280° ∴ angle ADB =(280°/2)=140°

Q. A chord subtends an angle $8 0^{\circ}$ at the centre of a circle. What is the angle subtended by the chord in the minor segment of the circle?

$14 0^{\circ}$

$14 5^{\circ}$

$7 0^{\circ}$

$11 0^{\circ}$

$∠ A CB = 8 0^{\circ}$
Reflex angle $A CB = 28 0^{\circ}$
$∴ ∠ A D B = \frac{28 0 ^{\circ}}{2} = 14 0^{\circ}$

Q. A chord subtends an angle 80∘ at the centre of a circle. What is the angle subtended by the chord in the minor segment of the circle?

140∘

145∘

70∘

110∘