A pair of tangents can be constructed to a circle inclined at an angle of 170°. Write ‘True’ or ‘False’ and justify your answer

Solution:

Construct two tangents from P to the circle with centre at Q and R

Now join OQ and OR

Here OQ and OR are the radii of the circle

∠OQP = ∠ORP = 90° as PQ and PR are the tangents to the circle at Q and R

∠OQP + ∠ORP = 180° …. (1)

From the angle sum property

∠QPR + ∠QOR + (∠OQP + ∠ORP) = 360°

From (1) we get

∠QPR + ∠QOR + 180° = 360°

∠QPR + ∠QOR = 180°

Here ∠QPR and ∠QOR < 180°

The angle given is 170° which is less than 180°

Therefore, the statement is true.

✦ Try This: A pair of tangents can be constructed to a circle inclined at an angle of 190°.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 11

NCERT Exemplar Class 10 Maths Exercise 10.2 Problem 4

A pair of tangents can be constructed to a circle inclined at an angle of 170°. Write ‘True’ or ‘False’ and justify your answer

Summary:

The statement “A pair of tangents can be constructed to a circle inclined at an angle of 170°” is true

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