Radius of the circle = 5cm

Distance of the point from the center = 13 cm.

The steps for construction are:

Step 1: With O as the center draw a circle of radius 5 cm.

Step 2: Mark a point P at a distance of 13 cm from O and join OP.

Step 3: Draw the perpendicular bisector of OP. Let it meet OP at M.

Step 4: With M as center and MO as radius, draw another circle.

Step 5: Let the two circles intersect at X and Y.

Step 6: Join PX and PY. They are required tangents.

Thus, this is the resulting figure.

To determine the length of the tangent, consider the triangle OXP and apply Pythagoras theorem to it:

√OX² + √PX² = OP

⇒ OX² + PX² = OP²

⇒ 5² + PX² = 13²

⇒ PX² = 13² - 5²

⇒ PX² = 169 – 25

⇒ PX² = 144

⇒ PX = √144

⇒ PX = 12 cm

Thus, the length of the tangents is 12cm.