An inscribed angle is formed when two secant lines intersect on a circle. In other words, the inscribed angle in a circle is formed when one of the end points of two chords in a circle meet in a point.
In the above picture, L ABC is the of the circle.
From the picture above,
BAC angle = BDC angle
CABangle = (1 / 2) BOC angle
CDB angle = (1 / 2) BOC angle
Another Formula for inscribed angle:
If we know the length of the minor arc, radius, the inscribed angle is found by:
Angle= `(90 L)/(pi* R)`
L is the length of the shortest arc BA
R is defined as radius.
From the circle diagram below, the chord CA has a length of 12 cm and center at O. The circle has a radius of 14 cm. Find the measure of the inscribed angle ABC.
1. First we calculate the central angle AOC. The triangle AOC is a isosceles triangle. Distance of OC = Distance of OA = radius = 14 cm. Here we use cosine law to find value of cos (angle AOC).
AC2 = OC2 + OA2 - 2 OC OA cos (angle COA)
2. Substitute the value of the angles AC, OC and AO in cos (angle AOC) as follows
cos(angle COA) = `[ 14^2 + 14^2- 122 ] / [28 * 14 ]`
= `62 / 98`
3. The measure of the angle COA is given by.
Angle COA = `arccos (62 / 98)`
According to the theorem described before, the size of angle CBA will be equal to half the size of angle COA.
Angle CBA = `(1/ 2) arccos (62 / 98)`
= 25.38 degrees.
Given that the central angle of circle is 50 degrees. Find the angle of inscribed circle.
Answer = 100 degree
Given that the central angle of circle is 120 degrees. Find the angle of inscribed circle.
Answer = 240 degree.