Question

Find the value of c, rounded to the nearest tenth

A. 11
B. 14.3
C. 37.6
D. 7.4

Answer 1

The value of c for he given figure is 7.4

Explanation:

Given figure of circle with two chords meeting outside the circle

Let The points A, D , E , C are on the circle

And The chords AB and CD meets at points B

The measure of AD = 20

The measure of BD = 10

So. The measure of AB = 20 + 10 = 30

The measure of CE = c

The measure of EB = 14

So, The measure of CB = c + 14

Now, From the property of circle

AB × BD = CB × EB

Or, ( AD +BD ) × BD = ( CE + EB ) × EB

Or, ( 20 + 10 ) × 10 = ( c + 14 ) × 14

or, 30 × 10 = c × 14 + 196

Or, 300 - 196 = c × 14

Or c × 14 = 104

∴ c =
`(104)/(14)`

I.e c = 7.4

Hence The value of c for he given figure is 7.4 Answer

Answer 2

D. The correct value of c = 7.4

Explanation:

According to Tangent-Secant theorem:

"When a tangent and a secant are drawn from one single external point to a circle, square of the length of tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment."

Here, the external length of tangent segment = 10

Also, the length of internal segment is 14 and c.

So, by the SECANT THEOREM:

`(10)^2  = 14 * c\\\implies c = (100)/(14) = 7.14`

or, c = 7. 1428

Now, rounding off the value of c = 7. 14 to the nearest tenth, we get

c = 7. 4

Hence the correct value of c = 7.4