plane and solid geometry

hello po, patulog po ako

1. two tangent lines drawn from an external point to a circle makes an angle of 60 degrees with each other. The distance from the external point to the center of the circle is 10 cm. Find the radius of the circle and the length of the tangent segment.

2. the radii of two circles, with no common point are 4 cm and 18 cm respectively. The portion of their common external tangent included between the points of tangency is 22 cm. Find the distance between their centers, Find the distance from the point of tangency of the smaller circle to the point where the line of centers and the tangent meet.

3. three circles are placed tangent to each other, in the order of size, so that their centers lie on the same straight line and a line tangent to the largest and smallest is also tangent to he middle circle. the diameters of the smallest and the middle circles are 10 cm and 15 cm, respectively. Find the diameter of the largest circle

Jhun Vert's picture

No. 1
 

plane_002-lines-tangent-to-circles.gif

 

$\sin 30^\circ = \dfrac{r}{10}$

$r = 5 ~ \text{cm}$   ←   radius of the circle
 

$\cos 30^\circ = \dfrac{T}{10}$

$T = 8.66 ~ \text{cm}$   ←   length of tangent