Chapter 10 : Tangents to a circle

Example 3. In the figure, ABC is an isosceles triangle in which AB = AC. A circle through B touches the side AC at D and intersect the side AB at P. If D is the midpoint of side AC, Then AB = 4AP.

Solution:- AP X AB = AD² = (1/2AC)²

AP X AB = 1/4 AC² [AD = 1/2AC]

Or, 4 AP.AB = AC² [AC = AB]

Or, 4 AP.AB = AB²

Or, 4 AP = AB

Example 4. In the figure. Find the value of AB Where PT = 5cm and PA = 4cm.

Solution:- PT² = PA X PB (Theory.2)

5² = 4 X PB

PB = 25/4 = 6.25

AB = PB - PA

AB = 6.25 - 4

AB = 2.25 cm