find the length of the tangent drawn from a point 6 cm from a circle whose radius is 9 cm.?

Question

a) 12 cm
b) 6 (square root of 2) cm
c) 8 cm
d) none of these

Answer 1

The answer is A) 12. If the point is 6 centimeters from the outside of the circle, then it is 15 cm from the center. There is a right triangle formed by the segment connecting the center to the outside point, the segment connecting the outside point to the point of tangency (this is the one we want to find the length of), and the radius from the center to the point of tangency. Using the pythagorean theorem, we get:

15^2 = 9^2 + x^2
225 = 81 + x^2
144 = x^2
x = 12

The mistake made by the previous answerers was substituting the two known values (15 and 9) in for a and b in the pythagorean theorem. However, 15 represents the hypotenuse of the triangle, so it should be substituted for c.

Answer 2

mathsmart is right

If C is the centre and P is the point 6 cm from the circle
CP = 6+9 = 15
If PQ is the required length of the tangent
CPQ is a right angled triangle with right angle at Q
therefore
PQ = sqrt{CP^2 - CQ^2}
= sqrt{15^2 - 9^2} note that CQ = radius =9}
= 12 cm

Answer 3

The radius of the circle is 9 cm and the tangent is drawn from 6 cm distance for the circumference of the circle.

The tangent is always perpendicular to the radius

Tha tangent is the hypotenuse of the triangle formed by the ponint to the cnetre ofthe circle and the point of contact of the tangent to the centre

Length of tangent = sq rt of 15^2+9^2
sq rt of 306
= 17.49 cm

Answer 4

12 cm by inspection.

It's a 3-4-5 right triangle

Answer 5

Mathsmart is exactly correct. The answer is a-12.

Answer 6

d) none of these

Answer: Square root(15squared + 9squared} = ca 17

Answer 7

its d....i think its square root of 141, but not positive. my math is a little rusty during the summer.

Answer 8

D. Not enough info. You have to make too many assumptions to get an answer.

Answer 9

D