If angle between two radii of a circle is 130º, the angle between the tangents at the ends of the radii is
a. 90°
b. 50°
c. 40°
d. 70°
Solution:
Given, the angle between two radii of a circle is 130°
We have to find the angle between the tangents at the ends of the radii.
Let OA and OB be the two radii of the circle.
Given, ∠AOB = 130°
PA and PB are the tangents of the circle.
We know that the tangent is perpendicular to the radius at the point of contact.
So, tangent PA is perpendicular to the radius OA of the circle.
Also, tangent PB is perpendicular to the radius OB of the circle.
∠OAP = 90° and ∠OBP = 90°
From the figure,
AOBP is a quadrilateral.
We know that the sum of angles of a quadrilateral is 360°
∠AOB + ∠OAP + ∠OBP + ∠APB = 360°
130° + 90° + 90° + ∠APB = 360°
130° + 180° + ∠APB = 360°
310° + ∠APB = 360°
∠APB = 360° - 310°
∠APB = 50°
Therefore, the angle between the tangents at the ends of the radii is 50°
Verification:
We know that the sum of opposite angles of a quadrilateral is 180°
∠AOB + ∠APB = 180°
130° + ∠APB = 180°
∠APB = 180°- 130°
∠APB = 50°
Therefore, the angle between the tangents is 50°
✦ Try This: If angle between two radii of a circle is 170º, the angle between the tangents at the ends of the radii is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.1 Sample Problem 1
If angle between two radii of a circle is 130º, the angle between the tangents at the ends of the radii is a. 90°, b. 50°, c. 40°, d. 70°
Summary:
If angle between two radii of a circle is 130º, the angle between the tangents at the ends of the radii is 50°
☛ Related Questions:
- In Fig. 9.1, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O . . . .
- In Fig. 9.2, PQ is a chord of a circle and PT is the tangent at P such that ∠QPT = 60°. Then ∠PRQ is . . . .
- If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle wh . . . .