Question

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, then determine the diameter of the circle that contains AH. (section 10.6 question 5 in geometry math nation)

Answer 1

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