A chord of a circle is equal to the radius of the circle Find the angle subtended by thre - Maths - Circles

Question

A chord of a circle is equal to the radius of the circle Find
the angle subtended by thre chord at a point on the minor arc and
also at a point on the major arc

Priyanka Kedia · Accepted Answer

Given that: A chord of a circle equal to its radius, So, In $Δ O A B$ , AB = OA = OB = radius of circle Thus, $Δ O A B$ is an equilateral triangle Therefore, each interior angle of this triangle will be of $60^{0}$ So, $∠ A O B = 60^{0}$ And, angle subtended at the centre of a circle by an arc is double the angle subtended by it on any point on the remaining part of the circle $∠ A C B = \frac{1}{2} ∠ A O B = \frac{1}{2} (60^{0}) = 30^{0}$ In cyclic quadrilateral ACBD, $∠ A C B + ∠ A D B = 180^{0} (O p p o s i t e a n g l e i n c y c l i c q u a d r i l a t e r a l) \Rightarrow ∠ A D B = 180^{0} - 30^{0} = 150^{0} \Rightarrow ∠ A C B = 180^{0} - 150^{0} = 30^{0}$ Therefore, angle subtended by the chord at a point on the major arc is $30^{0}$ and on minor arc is $150^{0}$

A chord of a circle is equal to the radius of the circle. Find the angle subtended by thre chord at a point on the minor arc and also at a point on the major arc.