2017 · Q63
AB and CD are parallel chords of a circle 3 cm apart. If AB = 4 cm, CD = 10 cm, then what is the radius of the circle ?
Elementary MathematicsCircles
- A7 cm
- B√(19) cm
- C√(29) cm
- D14 cm
Explanation
Let the centre be at distance y from chord CD (length 10), with AB (length 4) on the opposite side, 3 cm away. Then R² = 25+y² = 4+(y+3)², giving 25+y² = y²+6y+13, so y = 2 and R² = 29. (Placing both chords on the same side yields no valid y.) Hence option (C) √(29) cm.