Two chords of a circle AB and CD meet at a point P outside the circle. If AP = 200 mm, AB = 120 mm, and CP =160 mm, then what is the length of CD?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 60 mm.
Given that
AP = 200 mm, AB = 120 mm, CP = 160 mm
BP = AP - AB = 200 - 120 = 80 mm
According to the question
⇒ CP × DP = AP × BP
⇒ 160 × DP = 200 × 80
⇒ DP = 200 × 80/160 = 100 mm
⇒ Hence, CD = CP - DP = 160 - 100 = 60 mm