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To measure the point at which two tangents intersect each other, find an equation for each tangent line and compute the intersection.
The tangent is the slope of a curve at a point. Knowing that slope and the coordinates of that point, you can determine the equation of the tangent line using one of the forms of a line such as point-slope, point-point, point-intercept, etc. Do the same for the other tangent. Solve the two equations as a system of two equations in two unknowns and you will have the point of intersection.
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What is the measure of the angle formed by two tangents drawn to a circle from an external point if they intersect a major arc whose measure is 200 degrees?
The angle between the two tangents is 20 degrees.
What is the measure of the angle formed by two tangents drawn to a circle from an external point if they intersect a minor arc whose measure is 80 degrees?
100 degrees
What is the measure of the angle formed by two tangents drawn to a circle from an external point if they intersect a minor arc whose measure is 150 degrees?
Assuming the measure of the arc refers to the angle at the centre of the circle, the answer is 180 - 150 = 30 degrees.
What is the measure of the angle formed by two tangents drawn to a circle from an external point if they intersect a major arc whose measure is 243 and the minor arc measures 117?
63o. Join the points where the tangents touch the circle to its centre to form a quadrilateral (two meeting tangents and two radii). These angles are both 90o, summing to 180o. Thus the other two angles - the one at the centre of the circle and the one where the tangents meet - sum to 360o - 180o = 180o (they are supplementary). The centre angle is given as 117o (the minor arc), so the angle where the tangents met is 180o - 117o = 63o.
What is orthogonal trajectories?
Two curves which intersect at right angles, ( the angle between the two tangents to the curve) curves at the point of intersection are called orthogonal trajectories. The product of the slopes of the two tangents is -1.
