To solve this problem, let's summarize the given information and then apply geometry principles step-by-step.

Given:

• Two circles touch each other at point A.
• Circle with center O has radius = 7 cm.
• Circle with center O' has diameter = 10 cm, so radius = 5 cm.
• Point P is at a certain distance from O (distance not explicitly given in your text; please confirm if you have this value).
• We need to find the length of the tangent PC from point P to one of the circles (presumably the circle with center O).

Step 1: Understand the configuration

• Since the two circles touch each other at point A , the distance between their centers O and O' is the sum of their radii:

OO′=7+5=12 cmOO'=7+5=12\text{ cm}OO′=7+5=12 cm

• Point P is located somewhere relative to O and O'.

Step 2: Clarify the position of point P

You mentioned:

p is a point which is at a distance of ... cm from o

The exact distance from P to O is missing in your query. This distance is essential to find the length of the tangent PC.

Step 3: Formula for tangent length from a point outside a circle

If P is a point outside a circle with center O and radius r , and the distance from P to O is d=POd=POd=PO, then the length of the tangent from P to the circle is given by:

PC=d2−r2PC=\sqrt{d^2-r^2}PC=d2−r2​

Step 4: Apply the formula

• If you provide the distance POPOPO, then:

PC=(PO)2−72=(PO)2−49PC=\sqrt{(PO)^2-7^2}=\sqrt{(PO)^2-49}PC=(PO)2−72​=(PO)2−49​

Summary

To find the length of the tangent PC , you need to know the distance from P to the center O of the circle with radius 7 cm. Once you have that distance ddd, use:

PC=d2−49PC=\sqrt{d^2-49}PC=d2−49​

If you can provide the exact distance POPOPO, I can calculate the exact length of the tangent for you!