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# The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle

**Solution:**

Let's draw a tangent from point A to the circle as shown below.

A tangent at any point of a circle is perpendicular to the radius through the point of contact.

Therefore, ∠OTA = 90° and ΔOTA is a right-angled triangle.

OA^{2} = OT^{2} + AT^{2}

5^{2} = OT^{2} + 4^{2}

OT^{2} = 25 - 16

OT^{2} = 9

OT = ± 3

Radius OT cannot be negative.

Hence, the radius is 3 cm.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 10

**Video Solution:**

## The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle

Maths NCERT Solutions Class 10 Chapter 10 Exercise 10.2 Question 6

**Summary:**

If the length of a tangent from a point A at distance 5 cm from the center of the circle is 4 cm, then the radius of the circle is 3 cm.

**☛ Related Questions:**

- 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(A) 7 cm(B) 12 cm(C) 15 cm(D) 24.5 cm
- In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to(A) 60°(B) 70°(C) 80°(D) 90°
- If tangents PA and PB from a point P to a circle with center O are inclined to each other at angle of 80°, then ∠POA is equal to(A) 50°(B) 60°(C) 70°(D) 80°
- Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

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