In Fig. 9.1, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is
a. 10 cm
b. 5 cm
c. 2 cm
d. 7 cm
Solution:
Given, AP and AQ are the tangents drawn from an external point A to a circle with center O.
The tangents are perpendicular to each other.
The length of each tangent is 5 cm.
We have to find the radius of the circle.
Given, ∠PAQ = 90°
We know that the radius is perpendicular to the tangent at the point of contact.
So, ∠APO = 90°
∠AQO = 90°
Consider triangle APO,
APO is a right triangle with P at right angle.
OP is the radius of the circle.
Given, ∠PAO = 45°
We know that tan A = opposite/adjacent
Here, opposite = OP
Adjacent = AP = 5 cm
tan 45° = OP/AP
By trigonometric ratio of angles,
tan 45° = 1
So, tan 45° = OP/AP becomes
1 = OP/5
OP = 5 cm
Therefore, the radius of the circle is 5 cm.
✦ Try This: A pair of tangents RP and RQ drawn from an external point R to a circle with centre O are perpendicular to each other and length of each tangent is 7 cm. Then the radius of the circle is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.1 Sample Problem 2
In Fig. 9.1, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is a. 10 cm, b. 5 cm, c. 2 cm, d. 7 cm
Summary:
In Fig. 9.1, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and the length of each tangent is 5 cm. Then the radius of the circle is 5 cm
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