Elio makes candles that are 14\text{ cm}14 cm14, start text, space, c, m, end text tall. Each candle burns 888 hours before going out. He is wondering how many hours a 21\text{ cm}21 cm21, start text, space, c, m, end text tall candle can burn for. He assumes that the relationship between the height of a candle and number of hours it burns (h)(h)left parenthesis, h, right parenthesis is proportional.
How long can a 21 \text{ cm}21 cm21, start text, space, c, m, end text tall candle burn for?

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12