Question

Find the length of the tangent to a circle with centre ‘O’ and radius 6 cm from a point P such that

OP = 10 cm​

Answer 1

Answer:

The length of the tangent can be find by using Pythagoras property

First draw radius on tangent in such a way that it falls at 90°.

This problem can be solve using Pythagoras Theorem.

This theorem is used for Right angle triangle. In right angle triangle if one of the side is unknown then we can find it by using formula:

(Hypotenuse)² = (Base)² + (Perpendicular)²

Firstly take the ΔOPQ, We have

OP = 10, OQ = 6 and QP = ?

⇒ (OP)² = (OQ)² + (QP)²

⇒ 100 = 36 + (QP)²

⇒ (QP)² = 100 - 36 = 64

⇒ QP = 8

Thus, tangent QP = 8 cm

Answer 2

Answer:

• 8 cm

Step-by-step explanation:

Given

• Radius of circle (OA) = 6 cm
• OP = 10 cm

To find

• Length of tangent (PA)

Solution

We know, tangent is perpendicular to the radius at the point of contact.

Here, PA is the tangent segment and OA is the radius of circle.

∴ OA ⊥ PA , ∠OAP = 90° and in ΔOAP:

• OP² = OA² + PA²

(Pythagoras theorem)

• 10² = 6² + PA²
• PA² = 100 - 36
• PA² =64
• PA = √64
• PA = 8

∴ PA or the length of the tangent is 8 cm.