Question

A secant and a tangent meet at a 90° angle outside the circle. What must be the difference between the measures of the intercepted arcs? 45° 90° 180° 270°.

Answer 1

The difference between the measures of the intercepted arcs of the given circle is 45°.

A circle is defined as the set of points in a plane equidistant to each, such that it forms a closed two-dimensional figure, which is known as a circle.

• A line intersecting a circle at a minimum of two distinct points is known as a secant and the line touching the circle at only one point, is known as the tangent of a circle.
• The intercepted arc is the section of the circumference of a circle such that it is either encased by two chords or a line segment, meeting at a single point.

We are given that the angle subtended by secant and tangent, outside the circle is,

$\theta =90^{\circ}$

And angle measured inside the circle is,

$\phi = \theta /2\\\\\phi = 90/2\\\\\phi = 45{^\circ}$

So, the difference between the measures of the intercepted arcs is,

$\theta' = \theta - \phi\\\\\theta' = 90-45\\\\\theta' =45^{\circ}$

Thus, we can conclude that the difference between the measures of the intercepted arcs of the given circle is 45°.

learn more about the tangent here:

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