Given three circles with centres O1, O2 and O3. OE and OF are the tangents drawn from an external point O to the three circles as shown in the figure below. OE = 24 cm, O3E = 2O2C = 4O1A = 7 cm. Find O2G : O1H. (Figure not drawn to scale)
Figure description: Two straight lines meet at an external point O, forming a narrow wedge. Three circles of decreasing size, centred at O3 (largest, farthest from O), O2 (medium), and O1 (smallest, nearest O), sit inside this wedge, each tangent to both slanted lines. The two tangent lines touch the largest circle at E (upper) and F (lower), the medium circle at C (upper) and D (lower), and the smallest circle at A (upper) and B (lower). The centres O3, O2, O1 and the point O all lie on one horizontal axis. The vertical line joining E and F crosses this horizontal axis at right angles at point G (between O3 and O2); the vertical line joining C and D crosses the axis at right angles at point H (between O2 and O1); the vertical line joining A and B crosses the axis at right angles at point I (between O1 and O).
