Question

the length of the tangents to a circle with radius 5 cm from a point which is 13 cm from the centre of the circle

Answer 1

Let the tangent be BC

Radius be AB

And the point from centre be AC

AB^2 + BC^2 = AC^2

5^2 + BC^2 = 13^2

25 + BC^2 = 169

BC^2 = 169 - 25

BC^2 = 144

BC = ROOT 144

BC = 12 cm

So the length of the tangent is 12cm.

Hope it helps you.

Answer 2

Hiii friend,

Let PA a tangent and P be a point from the center of the circle.

OP (H) = 13 cm

Radius OA (P) = 5 cm

By pythagoras theroem,

(H) = (B)² + (P)²

(OP)² = (PA)² + (OA)²

(PA)² = (OP)² - (OA)²

(PA)² = (13)² - (5)² => 169 - 25 => 144

PA = ✓144 = 12 cm


Therefore,

Length of tangent PA = 12 cm


HOPE IT WILL HELP YOU.... :-)