A circle with radius 1 has diameter AB. C lies on this circle such that $\frac{\widehat{A C}}{\widehat{B C}}$ = 4. $\overline{A C}$ divides the circle into two parts, and we will label the smaller part Region I. Similarly, $\overline{B C}$ also divides the circle into two parts, and we will denote the smaller one as Region II. The difference between the areas of Region I and II is : (where $\widehat{A C}$ represents are AC, $\overline{A C}$ represents chord AC)

Circles

Grade 11

Question:

A circle with radius 1 has diameter AB. C lies on this circle such that $\frac{\widehat{A C}}{\widehat{B C}}$ = 4. $\overline{A C}$ divides the circle into two parts, and we will label the smaller part Region I. Similarly, $\overline{B C}$ also divides the circle into two parts, and we will denote the smaller one as Region II. The difference between the areas of Region I and II is : (where $\widehat{A C}$ represents are AC, $\overline{A C}$ represents chord AC)

$\frac{4 \pi}{10}$

$\frac{3 \pi}{8}$

$\frac{3 \pi}{10}$

$\frac{ \pi}{4}$

Step-by-Step Solution

Key Concept: Determine the central angles for chords AC and BC using the given arc ratio and calculate the difference between their circular segment areas using the formula $A = \frac{1}{2}r^2(\theta - \sin\theta)$.

$\frac{3 \pi}{10}$

Correct Answer: C

Question:

Step-by-Step Solution

Master Circles with Mathbee