All categories

2 years ago

prove that if two circles are tangent externally then the common internal tangent bisects a common external tangent.

Mathematics

1 answer:

Scilla [17]2 years ago

5 0

Explanation:

Consider the attached diagram.

Circles A and B have mutual tangents CF and DE that intersect at point F.

We know that the two tangents to a circle from an external point are congruent, so ...

FE≅ FC

FD ≅ FC

By the transitive property of congruence, both segments congruent to FC are congruent to each other:

FD ≅ FE

Therefore, CF is a bisector of DE.

You might be interested in

Find the area A: 54.94 cm B: 40.59 cm C: 33.165 cm D: 27.47 cm

aleksandrvk [35]

D: 27.47 cm. A=b×h÷2

6.7×8.2=54.94
54.94÷2=27.47 cm

hey what can I say except your welcome.

8 0

2 years ago

Read 2 more answers

In the figure below, ∠ABC ≅ ∠DEC and ∠GFE ≅ ∠DCE. Point C is the point of intersection between segment AG and segment BD, while

I am Lyosha [343]

Answer:

See Below.

Step-by-step explanation:

We are given that:

$\angle ABC \cong \angle DEC\text{ and } \angle GFE \cong \angle DCE$

By vertical angles:

$\displaystyle \angle DEC\cong \angle GEF\text{ and } \angle DCE\cong \angle ACB$

Hence, by substitution:

$\displaystyle \angle ABC\cong \angle GEF\text{ and } \angle GFE\cong \angle ACB$

Then by Angle-Angle Similarity:

$\Delta ABC \sim \Delta GEF$

8 0

2 years ago

If f(x) and its inverse function, f(x), are both plotted on the same coordinate plane, where is their point of intersection?

Tcecarenko [31]

Answer:

(2,2)

Step-by-step explanation:

The graph of a function and that of its inverse should be always symmetric around the line y = x (goes at 45 degrees and crosses the origin of coordinates).

Therefore any intersection of the graphs must lie on the line y = x, which forces the x value of the intersection point to be the same as the y-value.

The only option shown where x and y have the same numerical value is the third listed option : (2,2)

7 0

2 years ago

Help please Brainiest answer to whoever is first Show work if you can

aalyn [17]

Answer:

114

Step-by-step explanation:

19x6=114

6 0

2 years ago

Read 2 more answers

Hannah loves to shop. She can shop in 1/9 of the mall in 1/4 of an hour. If she continues at this rate, how much of the mall can

DiKsa [7]

4/9s of the mall per hour. 1/9 + 1/9 + 1/9 + 1/9

7 0

2 years ago