Question

If a point p is 17cm from the center of curcle of radius 8cm find length of the tangents drawn to the circle from point p​

Answer 1

Answer:

15 cm

Step-by-step explanation:

let the point of contact be A

center of circle be O

the tangent make a 90° at point of contact A

radius of circle = OA = 8 cm

distance from center to point P = OP = 17 cm

we need to find the length of tangent = PA

we use Pythagoras theorem

${op}^{2} = {pa}^{2} + {oa}^{2} \\ {17}^{2} = {pa}^{2} + {8}^{2} \\ 289 = {pa}^{2} + 64 \\ {pa}^{2} = 289 - 64 \\ {pa}^{2} = 225 \\ pa = \sqrt{225} = 15$

length of tangent PA = 15 cm

hope you get your answer