Answer:
4(x+4)
Step-by-step explanation:
Find to GCF of 4x+16.
Now factor out the GCF by dividing each term in the expression by 4.
4x divided by the GCF is x, and 16 divided by the GCF is 4.
The equivalent expression is 4(x+4).
OK. I did it. Now let's see if I can go through it without
getting too complicated.
I think the key to the whole thing is this fact:
A radius drawn perpendicular to a chord bisects the chord.
That tells us several things:
-- OM bisects AB.
'M' is the midpoint of AB.
AM is half of AB.
-- ON bisects AC.
'N' is the midpoint of AC.
AN is half of AC.
-- Since AC is half of AB,
AN is half of AM.
a = b/2
Now look at the right triangle inside the rectangle.
'r' is the hypotenuse, so
a² + b² = r²
But a = b/2, so (b/2)² + b² = r²
(b/2)² = b²/4 b²/4 + b² = r²
Multiply each side by 4: b² + 4b² = 4r²
- - - - - - - - - - -
0 + 5b² = 4r²
Repeat the
original equation: a² + b² = r²
Subtract the last
two equations: -a² + 4b² = 3r²
Add a² to each side: 4b² = a² + 3r² . <=== ! ! !
By dropping a perpendicular from the top of the isosceles triangle to the base and using the Pythagorean Theorem we quickly determine that the height of the triangle is 4.
Therefore the area of the isosceles triangle is
6•4/2=12
However, we can split the isosceles triangle into three separate triangles indicated by the red lines in the diagram below. Because the radius always meets a tangent at a right angle the area of each triangle will be the length of the side multiplied by the radius of the circle. So the total area of the isosceles triangle is given by
6r/2+2•5r/2=8r=12
8r=12
r=12/8
r=3/2
Given:
In the circle P, ABCD is inscribed quadrilateral.
And, ∠DAB = 110°, ∠ABC = 72°
To find the value of ∠ADC.
Theorem:
A quadrilateral can be inscribed in a circle if and only if the opposite angles are supplementary [ sum of the opposite angles will be 180°]
According to the theorem,
Hence,
The value of ∠ADC is 108°.
Hence, Option b is the correct answer.
