Question

Type in the value of x if diameter TV is a segment bisector of chord EF and mTKF=5(x 7)

Answer 1

If diameter TV is a segment bisector of chord EF, it means that TKF is a right angle, because a diameter of a circle always bisects any chord it intersects at a right angle.

Given that m(TKF) = 5(x + 7), and TKF is a right angle, we know that m(TKF) must be 90 degrees.

So, we have:

\[ 5(x + 7) = 90 \]

Now, let's solve for \(x\):

\[ x + 7 = \frac{90}{5} \]
\[ x + 7 = 18 \]
\[ x = 18 - 7 \]
\[ x = 11 \]

Therefore, the value of \(x\) is 11.

Answer 2

Answer:

To solve for \( x \), given that diameter \( TV \) bisects chord \( EF \) at point \( K \) and that the measure of angle \( m\angle TKF \) is \( 5(x + 7) \), we need to consider a few properties of circles:

1. A diameter that bisects a chord is perpendicular to the chord.

2. If a diameter bisects a chord, it also bisects the angle formed by the chord and a point on the circle through which the diameter passes.

Therefore, if \( TV \) is the diameter and it bisects \( EF \) at \( K \), then \( TK \) and \( KV \) are radiuses of the circle and \( TK \) is perpendicular to \( EF \). The triangle \( TKF \) is a right triangle at \( K \).

The angle \( m\angle TKF \) is actually \( 90^\circ \) because \( TK \) is perpendicular to \( EF \). Therefore, setting up the equation based on your input:

\[ 5(x + 7) = 90 \]

We can solve this equation to find \( x \). Let's do that calculation.

The value of \( x \) is 11.

Step-by-step explanation: