In the circle below, the chord  is extended to meet the tangent  at D. If  = 9 cm and  = 3 cm, find the length of .

This question was previously asked in
RRC Group D Previous Paper 24 (Held On: 20 Sept 2018 Shift 2)
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  1. 5 cm
  2. 4 cm
  3. 6 cm

Answer (Detailed Solution Below)

Option 4 : 6 cm
Free
RRB Group D Full Test 1
100 Qs. 100 Marks 90 Mins

Detailed Solution

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Given:

AB = 9 cm

BD = 3cm

Concept Used:

If DBA is the intersecting line of the circle which intersects the circle at A and B and DE is a tangent, then

DE2 = AD × BD

Calculation:

According to the question,

DE2 = AD × BD

⇒ DE2 = (AB + BD) × BD

⇒ DE2 = (9 + 3) × 3

⇒ DE2 = √36 = 6

⇒ DE = 6

∴ The Length of DE = 6 cm.

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