Question

The length of the tangent drawn from a point
8cm away from the centre of the circle with
radius 6cm is
​

Answer 1

Answer:

Let O be the centre of the circle. OA is the radius of the circle and OP is 8 cm

According to question, we have

∠OAP=90

0

So,cby Pythagoras theorem,cwe get

OP

2

=OA

2

+AP

2

⇒AP

2

=OP

2

−OA

2

⇒AP

2

=8

2

−6

2

⇒AP

2

=64−36

⇒AP

2

=28

⇒AP=2√7cm

Answer 2

❖ Given :-

• length of tangent OQ = 8cm
• Length of radius OP = 6cm

❖ To Find :-

• Length of PR

❖ Solution :-

Since, PR | OP (Tangent at any point if circle is prependicular to the radius through point of contact)

∴ Angle OPQ = 90°

∴ ∆ OPQ is a right angled triangle.

Now, in ∆ OPQ,

(OQ)² = (OP)² + (PQ)²

Substituting the values, we get :-

(OQ)² = (6)² + (8)²

(OQ)² = 36 + 64

(OQ)² = 100

OQ = $\sqrt{100}$

$\huge{\purple{\underbrace{\overbrace{\red{OQ\: =\: 10\:cm}}}}}$