Tangent to Circle

NCERT Exercise

10.2 Part 1

Question: 1 - From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. the radius of the circle is:

  1. 7 cm
  2. 12 cm
  3. 15 cm
  4. 24.5 cm

Answer:(a) 7 cm




Explanation: Here; PQ = 24 cm, OQ = 25 cm, OP = ?

Tangent to a Circle

In ΔOPQ

`OQ^2 = OP^2 + PQ^2`

Or, `OP^2= OQ^2 – PQ^2`

`= 25^2 – 24^2`

`= 625 – 576 = 49`

Or, `OP = 7` cm




Question: 2 - In the given figure; if TP and TQ are two tangents to a circle with centre O so that ∠POQ=110°, then ∠PTQ is equal to

  1. 60°
  2. 70°
  3. 80°
  4. 90°

Answer: (b) 70°




Explanation: Here; `∠OPT = ∠OQT = 90°` (Since radius is perpendicular to tangent)

Two Tangents and a Circle

Hence, `∠POQ + ∠PTQ = 180°`

Or, `110° + ∠PTQ = 180°`

Or, `∠PTQ = 180° - 110°`

Or, `∠PTQ = 70°`





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