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:
- 7 cm
- 12 cm
- 15 cm
- 24.5 cm
Answer:(a) 7 cm
Explanation: Here; PQ = 24 cm, OQ = 25 cm, OP = ?
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)
Hence, `∠POQ + ∠PTQ = 180°`
Or, `110° + ∠PTQ = 180°`
Or, `∠PTQ = 180° - 110°`
Or, `∠PTQ = 70°`