Multiple choice

In a circle, chords PQ and TS are produced to meet at R. If RQ = 14.4 cm, PQ = 11.2 cm, and SR = 12.8 cm, then the length of chord TS is:

  1. 18 cm

  2. 14.2 cm

  3. 12.4 cm

  4. 16 cm
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D Correct answer
Explanation

By the Intersecting Secants Theorem, RQ * RP = RS * RT. Given RQ=14.4, PQ=11.2, then RP = 14.4 + 11.2 = 25.6. RS=12.8. So 14.4 * 25.6 = 12.8 * RT. RT = (14.4 * 25.6) / 12.8 = 14.4 * 2 = 28.8. TS = RT - RS = 28.8 - 12.8 = 16.

AI explanation

When two secants are drawn from an external point, the secant and external segment product identity states that RQ times RP equals SR times RT. Given RQ is 14.4 cm and PQ is 11.2 cm, the entire segment RP is 14.4 + 11.2 = 25.6 cm. Using the given SR of 12.8 cm, we write the equation 14.4 * 25.6 = 12.8 * RT, which simplifies to RT = 28.8 cm. The length of chord TS is found by subtracting SR from RT, resulting in 28.8 - 12.8 = 16 cm.

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