The secant CD intersects the circle at E and CF is tangent to the circle at F. If the length of the secant CD is equal to 20 cm and the length of tangent CF is 15 cm, find the length of the chord DE.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 8.75 cm.
According to the given question,
CD × CE = CF2
⇒ 20 × CE = 152
⇒ 20 × CE = 225
⇒ CE = 11.25 cm
Now, CD = CE + DE
⇒ DE = CD - CE
⇒ DE = 20 - 11.25
⇒ DE = 8.75 cm
Hence the length of the chord DE is 8.75 cm.