Two circles of radii 3.5 and 4.2 cm with centres O1 and O2 intersect at points A and B as shown. The distance between the two centres is 6 cm. Calculate: (a) The size of angle AO1B. (b) The size of angle AO2B. (c) The area of quadrilateral O1AO2B. (d) The shaded area.

Question

Two circles of radii 3.5 and 4.2 cm with centres O1 and O2 intersect at points A and B as shown. The distance between the two centres is 6 cm. Calculate: (a) The size of angle AO1B. (b) The size of angle AO2B. (c) The area of quadrilateral O1AO2B. (d) The shaded area.

Asked on March 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-26T04:43:12.570Z

Step 1: Identify the given information from the problem. Radius of circle with centre $O_1$ is $r_1 = O_1A = O_1B = 3.5$ cm. Radius of circle with centre $O_2$ is $r_2 = O_2A = O_2B = 4.2$ cm. Distance between centres $O_1O_2 = 6$ cm. Points A and B are the intersection points of the two circles. a) The size of $\angle AO_1B$ (to the nearest degree) Consider the triangle $\triangle AO_1O_2$. The sides are $O_1A = 3.5$ cm, $O_

Accepted Answer · 2026-03-26T04:43:12.570Z

Step 1: Identify the given information from the problem. Radius of circle with centre $O_1$ is $r_1 = O_1A = O_1B = 3.5$ cm. Radius of circle with centre $O_2$ is $r_2 = O_2A = O_2B = 4.2$ cm. Distance between centres $O_1O_2 = 6$ cm. Points A and B are the intersection points of the two circles. a) The size of $\angle AO_1B$ (to the nearest degree) Consider the triangle $\triangle AO_1O_2$. The sides are $O_1A = 3.5$ cm, $O_