Question

Does anyone know the answer In the diagram of circle O, what is the measure of ∠ABC?

Answer 1

Answer:

54 degrees

Step-by-step explanation:

Given is a circle O.

The centre is O.

Angle AOC = 126

AB and BC are tangents to the circle

COnsider the quadrilatral ABCO.

Since AB and BC are tangents they both are perpendicular to their corresponding radius.

IN quadrilateral ABCO,we have two angles 90 degrees and one angle AOC=126

Since sum of angles = 180

we have angle ABC = 360-(90+90+126)=54 degrees

Answer 2

Answer: The measure of ∠ABC = 54°.

Step-by-step explanation:

As we know that

Measure of major arc AC = 234° ( Far arc)

Measure of minor arc AC = 126° (Near arc)

By theorem, we know that the angle formed by intersection of two tangents is equal to half the difference of far arc and near arc.

As we know that ∠ABC is given by

$\frac{1}{2}(Far\ arc-Near\ arc)\\\\=\frac{1}{2}(234-126)\\\\=\frac{1}{2}\times 108^\circ\\\\=54^\circ$

Hence, the measure of ∠ABC = 54°.