Given:
The scale factor between two circles is .
To find:
The ratio of their areas.
Solution:
We know that, all circles are similar.
The ratio of the areas of similar figures is equal to the ratio of squares of their corresponding sides or equal to the square of ratio of their corresponding sides.
The scale factor is the ratio of the corresponding sides.
Ratio of areas of circles = Square of scale factor between two circles
Therefore, the correct option is D.
Answer:
Step-by-step explanation:
From the picture attached,
a). Triangle in the figure is ΔBCF
b). Since, and
are the parallel lines and m is a transversal line,
m∠FBC = m∠BFG [Alternate interior angles]
Since, and
are the parallel lines and n is a transversal line,
m∠BCF = m∠CFE [Alternate interior angles]
By triangle sum theorem in ΔBCF
m∠FBC + m∠BCF + m∠BFC = 180°
From the properties given above,
m∠BFG + m∠CFE + m∠BFC = 180°
m∠GFE = 180°
Therefore, angle GFE is the straight angle that will be useful in proving that the sum of the measures of the interior angles of the triangle is 180°.