Question

PT is the tangent from point P to a circle with cente O and radius 5 cm at t if OP=13 cm then find the length of PT​

Answer 1

Answer:

12 cm

Step-by-step explanation:

Triangle OPT is right angled at T

Hypotenuse = 13 cm

Height = 5 cm

Therefore, Base = 12 cm (From Pythagoras' Theorem)

Answer 2

Value of PT is 12 cm if PT is the tangent from point P to a circle with center O and radius 5 cm at T and OP = 13 cm

Given:

• PT is tangent from point P to circle with center O
• Radius 5 cm
• OP = 13 cm

To Find:

• Length of PT

Solution:

• Tangent at a point on circle is perpendicular to radius on that point

Pythagorean theorem:

Square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.

Step 1:

OT is radius hence

OT = 5 cm

Step 2:

ΔOTP is right angle triangle at T as PT is tangent and OT is radius

Hence Perpendicular sides are OT and PT and OP is hypotenuse

Step 3:

Apply  Pythagorean theorem:

OP² = OT² + PT²

Step 4:

Substitute OP = 13 cm , OT = 5 cm and solve for PT

13² = 5² + PT²

=> 169 = 25 + PT²          (Calculate square on number)

=> 144 = PT²                 (subtract 25 from both sides)

=> 12 = PT                (taking square root both sides and considering positive value only as length can not be negative)

Value of PT is 12 cm