Question

In the diagram below, DE and Ef are tangent to o. Which expression gives
the measure of DEF?

Answer 1

Answer:

A

Step-by-step explanation:

∠DEF is a tangent- tangent angle and is measured as

∠DEF = $\frac{1}{2}$( arc GF - arc DF), that is

∠DEF = $\frac{1}{2}$(236 - 124)° → A

Answer 2

The expression which gives the measure of DEF, in the diagram where, DE and Ef are tangent to circle o is 1/2(236-124) degrees.

What is the theorem of two tangents from external point?

When the two tangent are drawn to a circle from an exterior point then according to this theorem-

The length of these two tangents is equal.

• Both the tangents subtend equal angle at the center of the circle.
• The angle between the two tangent is bisect by the line joining to the exterior point and the center.

In the diagram below, DE and EF are tangent to o.  In the diagram half of the difference of the arc GF and DF is equal to the angle of the measure of DEF. Thus,

$\angle DE F=\dfrac{1}{2}(GF-DF)\\\angle DE F=\dfrac{1}{2}(236-124)$

Thus, the expression which gives the measure of DEF, in the diagram where, DE and Ef are tangent to circle o is 1/2(236-124) degrees.

Learn more about the theorem of two tangents from external point here;

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