To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is
a. 105°
b. 70°
c. 140°
d. 145°
Solution:
Consider PA and PB as the two tangents drawn inclined at an angle 35°
We know that
At the point of contact, tangent and the radius are perpendicular
From the figure
∠OBP = ∠OAP = 90°
In the quadrilateral AOBP
∠AOB + ∠OBP + ∠OAP + ∠APB = 360°
Substituting the values
∠AOB + 90° + 90° + 35° = 360°
So we get
∠AOB + 215° = 360°
∠AOB = 145°
Therefore, the angle between the two radii of the circle is 145°.
✦ Try This: To draw a pair of tangents to a circle which are inclined to each other at an angle of 45°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 11
NCERT Exemplar Class 10 Maths Exercise 10.1 Sample Problem 2
To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is a. 105°, b. 70°, c. 140°, d. 145°
Summary:
To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is 145°
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