Two tangents drawn to a circle from an external point intercept a minor arc of 150°. What is the measure of the angle formed by these two tangents?
A1 = 150o = Minor Arc.
A2 = 360-150 = 210o = Major Arc.
X = (A2-A1)/2 = (210-150)/2 = 30o=Angle
formed by 2 tangents.
a
To find the measure of the angle formed by the two tangents, we need to use the property that tangents drawn from an external point to a circle are equal in length.
Let's call the angle formed by the tangents θ.
Since the tangents intercept a minor arc of 150°, we know that the measure of the angle at the center of the circle is twice that, which is 300°.
Now, we can use the fact that the angles of a triangle add up to 180° to find θ.
Since the sum of the angles in a triangle is 180°, we have:
θ + 90° + 90° = 180°
Combining like terms, we get:
θ + 180° = 180°
Subtracting 180° from both sides, we get:
θ = 0°
Therefore, the measure of the angle formed by the two tangents is 0°.
To find the measure of the angle formed by the two tangents, we can use the fact that tangents drawn from an external point to a circle are equal in length.
Let's call the two tangents AB and AC, with point A being the external point and B and C being the points where the tangents intersect the circle.
Since AB and AC are tangents, they are equal in length. This means that triangle ABC is an isosceles triangle, with AB = AC.
Now, let's consider the minor arc BC intercepted by the tangents. The measure of an arc is equal to the measure of its central angle. In this case, the minor arc BC has a measure of 150°.
Since BC is an arc, it is subtended by angle ABC at the center of the circle. Therefore, the measure of angle ABC is also 150°.
Since ABC is an isosceles triangle, its base angles are congruent. Therefore, angle BAC is also 150°.
Thus, the measure of the angle formed by the two tangents is 150°.