Do R2, R3, and R4 form a series or parallel circuit? Find all voltage drops, total

Explanation:

R₃ and R₄ are in series.  Their combined resistance is:

R₃₄ = R₃ + R₄

R₃₄ = 1500 Ω

This resistance is in parallel with R₂.  The combined resistance is:

1/R₂₃₄ = 1/R₃₄ + 1/R₂

R₂₃₄ = 750 Ω

This resitance is in series with R₁.  The total resistance is:

R = R₂₃₄ + R₁

R = 1000 Ω

Using Ohm's law, the total current is:

V = IR

I = 0.1 A

The voltage drop across R₁ is:

V = IR

V₁ = 25 V

The voltage drop across R₂ is:

V₂ = 100 V − V₁

V₂ = 75 V

The voltage drop across R₃ is:

V₃ = V₃₄ R₃ / R₃₄

V₃ = 25 V

The voltage drop across R₄ is:

V₄ = V₃₄ − V₃

V₄ = 50 V

Using Ohm's law, the current through each resistor is:

I₁ = 0.1 A

I₂ = 0.05 A

I₃ = 0.05 A

I₄ = 0.05 A

we know that

the intersecting chords theorem states that when two chords intersect each other inside a circle, the products of their segments are equal.

so

in this problem

substitutes the values

the length of segment vt is equal to

substitute the value of x

therefore

the answer is