Class 10 Mathematics

Circle

Exercise 10.2 (NCERT) 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:

  • 7 cm
  • 12 cm
  • 15 cm
  • 24.5 cm

Answer:(a) 7 cm


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

10 circle exercise solution

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

  • 60°
  • 70°
  • 80°
  • 90°

Answer: (b) 70°


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

10 circle exercise solution

Hence, `∠POQ + ∠PTQ = 180°`

Or, `110° + ∠PTQ = 180°`

Or, `∠PTQ = 180° - 110°`

Or, `∠PTQ = 70°`


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Circle Theorem

Exercise 10.1

Exercise 10.2 - Part 2

Exercise 10.2 - Part 3

Exercise 10.2 - Part 4

Exercise 10.2 - Part 5

Exercise 10.2 - Part 6