A, B and C are points on a circle, center O.
(a) Draw a tangent to the circle at point A.
(b) The circumference of the circle is 22.3 cm. Calculate the radius of the circle.
(c) Give a geometrical reason why angle BCA is 90°.
▶️ Answer/Explanation
Ans:
(a) A line perpendicular to radius OA at point A
(b) r = C/(2π) = 22.3/(2×3.142) ≈ 3.55 cm
(c) Angle in a semicircle is always 90°
The diagram shows a small circle with radius 7cm and a large circle with radius Rcm.
The area of 16 small circles is the same as the area of one large circle.
Calculate the value of R.
▶️ Answer/Explanation
Ans: 28
Area of one small circle: \( \pi (7)^2 = 49\pi \).
Total area of 16 small circles: \( 16 \times 49\pi = 784\pi \).
Area of large circle: \( \pi R^2 \). Set equal to \( 784\pi \).
Solve for \( R \): \( R^2 = 784 \), so \( R = \sqrt{784} = 28 \).