Answer:
Diameter of the circle = 7
Step-by-step explanation:
The exact question is as follows :
Given - The prom is in need of a floral archway, such as the one below. Segment RC is the perpendicular bisector of segment AH. If AH=6 and RC=2
To find - determine the diameter of the circle that contains AH.
Proof -
Given that,
AH = 6
RC = 2
Let us denote,
CB = x
So,
RB is the radius of the circle. It gives the value x + 2
As AH = 6
⇒AC = CH = 3
Also,
BH is the radius,
So, BH = x + 2
Now,
In triangle CBH,
BH² = CB² + HC²
⇒(x+2)² = x² + 3²
⇒x²+2² + 4x = x² + 9
⇒4 + 4x = 9
⇒4x = 9 - 4
⇒4x = 5
⇒x = 5÷4
⇒x = 1.5
So,
Radius = x + 2
= 1.5 + 2 = 3.5
⇒Radius = 3.5
As we know,
Diameter = 2×Radius
= 2×3.5
= 7
⇒Diameter of the circle = 7
The Pythagoras is the sum of the square of two sides is equal to the square of the longest side. Then the diameter of the circle is 6.5 units.
It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
The prom is in need of a floral archway, such as the one below.
Segment RC is the perpendicular bisector of segment AH.
If AH = 6 and RC = 2.
Let CB be x.
Then the radius RB will be x + 2
BH = x + 2
Then by the Pythagoras theorem, we have
BH² = CB² + HC²
⇒ (x + 2)² = x² + 3²
⇒x² + 4 +4x = x² + 9
⇒ 4x = 5
⇒ x = 1.25
The radius will be
r = x + 2
r = 1.25 + 2
r = 3.25
Then the diameter will be
Diameter = 2 × r
Diameter = 2 × 3.25
Diameter = 6.5
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
