Advertisements
Advertisements
प्रश्न
In the given figure, it is given that O is the centre of the circle and ∠AOC = 150°. Find ∠ABC.
Advertisements
उत्तर
It is given that O is the centre of circle and A, B and C are points on circumference.
`angle AOC = 150°` (Given)
We have to find ∠ABC
The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
\[\angle ABC = \frac{1}{2}\left( \text{ reflex } \angle AOC \right)\]
\[ = \frac{1}{2}\left( 360° - 150° \right)\]
\[ = \frac{1}{2} \times 210° \]
\[ = 105° \]
Hence,`angle ABC = 105°`
APPEARS IN
संबंधित प्रश्न
Fill in the blank:
Segment of a circle is the region between an arc and .................. of the circle.
Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.
Given an arc of a circle, show how to complete the circle.
If O is the centre of the circle, find the value of x in the following figure:
O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that ∠BOD = ∠A.
Prove that the angle in a segment greater than a semi-circle is less than a right angle.
In a circle, the major arc is 3 times the minor arc. The corresponding central angles and the degree measures of two arcs are
If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.
In the following figure, ∠ACB = 40º. Find ∠OAB.
