DE is a chord and KDE is a secant of a circle. If KD = 9 cm, DE = 7 cm and KH is a tangent to the circle at point H, then find KH.

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SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 1)
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  1. 12 cm
  2. 25 cm
  3. 16 cm
  4. 144 cm

Answer (Detailed Solution Below)

Option 1 : 12 cm
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PYST 1:SSC CGL 2023 - Quantitative Aptitude(Held On:14 Jul 2023 Shift 1)
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Detailed Solution

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Given:

DE is the chord of a circle.

KD = 9 cm ; DE = 7 cm

Concept used:

If a tangent and a secant are drawn from a common point outside the circle then,

Tengent2 = line of secant × (line of sacant - chord) 

Calculation:

F3 SSC Arbaz 17-10-23 D2

From tangent and secant relation:

⇒ KH2 = KD × KE

⇒ KH2 = 9 × 16

⇒ KH = √144 = 12 cm

∴ The correct answer is 12 cm. 

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