Question

Find the length of the tangent to the circle with center O and radius 6cm from a point P such that OP is 10cm

Answer 1

here,o is centre and let oq be perpendicular to the tangent op.so oq=6cm=radius and op=10cm.
by Pythagoras theorem,
(op)2=(oq)2+(qp)2
(10)2=(6)2+(qp)2
100=36+(qp)2
100-36=(qp)2
qp2=64

$qp = \sqrt{64}$
qp=8cm

Answer 2

Answer:

tangent QP = 8 cm

Step-by-step explanation:

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