https://file.aiquickdraw.com/mathbot/file/1732557799372a8s13tcd.jpg

### Solution:

#### Part (a): **The Length \( C_1C_2 \)**
From the diagram, we can calculate the distance \( C_1C_2 \) using the law of cosines:

\[
C_1C_2 = \sqrt{r_1^2 + r_2^2 - 2r_1r_2\cos(\angle ACB)}
\]

Where:
- \( r_1 = 10 \, \text{cm} \)
- \( r_2 = 7 \, \text{cm} \)
- \( \angle ACB = 50^\circ \), converted to radians: \( \angle = \frac{50\pi}{180} \approx 0.8727 \, \text{radians} \).



The figure below shows two intersecting circles with centres C1 and C2. Angle ACB = 50°. Then radii of the two circles are 10 cm and 7 cm respectively (Use π = 22/7). Calculate correct to 4 decimal places:
  a) The length C1C2;
  b) The area of the shaded region.

Solve a problem involving two intersecting circles with centers C1 and C2, radii 10 cm and 7 cm, and an included angle of 50°. Learn to find the length between centers and the area of the shaded region using the Law of Cosines and sector area calculations.

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