Question

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O

12 cm. Lenght PQ is:​
will be mark brainlest ​

Answer 1

Given :

• PQ is the tangent at point P
• OP is the radius through point of contact.

Find :

• Find the length of PQ

Solution :

By Tangent Radius Theorem , we know

OP is perpendicular to PQ

$\implies{ \angle OPQ = 90^{\circ}}$

By using Pythagoras Theorem :-

In Right Angle Triangle OPQ

OQ² = OP² + PQ²

→ OQ² - OP² = PQ²

→ PQ = √OQ² - OP²

Here , we know

• OQ = 12 cm
• OP = 5 cm

Substituting the values in it ,. we get :

→ √(12)² - (5)²

→ √144 - 25

→ √119

Therefore, the length PQ of tangent is √119 cm.

Answer 2

$\bold{\underline{Question-}}$

seems like a mistake in your question the correct question is A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

$\bold{\underline{Answer-}}$

$\bold{ √119 }$

$\bold{\underline{Explanation-}}$

According to the question we know that A tangent is PQ at a point of p of the circle at the radius 5cm meets a line through the centre O at point Q and OQ = 12

Need to find length PQ

now,

in ΔPOQ

Here angle P is right angle and we know that right angle is always 90°

so,

Using the Pythagoras theorem

OQ² = PQ² + OP²

now, transfer the PQ² in right side

PQ² = OQ² - OP²

now, putting the above values we get

PQ² = (12)² - (5)²

PQ² = 144 - 25

PQ² = 119

PQ = √119

Therefore , the length PQ of tangent is √119.