Two chords AB and CD of a circle meet inside the circle at point P. If AP = 12 cm, AB = 20 cm and CP = 16 cm, then CD = ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 22 cm.
given:
AP = 12 cm
AB = 20 cm,
so PB = AB − AP = 20 − 12 = 8 cm
CP = 16 cm
Let PD = xcm.
Then the length of the chord CD will be CD = CP + PD = 16 + x cm.
According to the Chord Intersection theorem:
AP × PB = CP × PD
12 × 8 = 16 × x
96 = 16x
x = 96/16 = 6cm
Now that PD = 6 cm, the length of CD is:
CD = CP + PD = 16 + 6 = 22 cm