Question

A point P is 13 cm from the center of the circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle

Answer 1

Answer:radius =5cm

Step-by-step explanation:by the tangenet make radius with 90°

By the point p is the hypotenuse

(since tangent format a triangle)

side^2+side^2=hypotenuse ^2

radius^2+12^2=13^2

x^2=13^2-12^2=169-144=25

x^2=25

x=5cm

There fore radius is 5cm

Answer 2

☣ Qᴜᴇsᴛɪᴏɴ ☣

➥ A point P is 13 cm from the center of the circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle

⛦ Aɴsᴡᴇʀ ⛦

➥ Radius of the Circle is 5 cm

☄ Gɪᴠᴇɴ ☄

➥ OP = 13 cm

➥ AP = 12 cm

⚛ Tᴏ Fɪɴᴅ ⚛

➥ Radius of Circle = ?

⠀⠀⠀⠀⠀⠀

❏ According To Given Question

⠀⠀⠀⠀⠀⠀

↗ We know that from any point P, outside the circle centre at O, makes a tangent at P where △OAP is right angled traingle and ∠OAP = 90°, so we can write OP is the hypotenuse of the right angled traingle and radius OA is the other side of the right angled traingle.

So, using Pythagoras theorem we can write,

OP² = AP² + OA²

⟾ 169 = 144 + OA²

⟾ OA² = 169 - 144

⟾ OA² = 25

⟾ OA² = $\displaystyle{\sf{\sqrt{25}}}$ = 5

Radius of the Circle (OA) = 5 cm