Question

ABC is an isosceles triangle with AB = AC = 4cm . A circle through B touches side AC at its middle point D and intersects side AB in point P. Find the value of AP

• A. 1 cm
• B. 4 cm
• C. 3 cm
• D. 2 cm

Answer 1

The correct option is A

1 cm

Since, AD is a tangent to the circle & BP is its chord intersecting the tangent AD at point A.

$A{D}^2$ = AP $\times$ AB

Since, D is the mid- point of AC

$\therefore$ AD = (1/2)AC = (1/2)AB

$\therefore$ $A{D}^2$ = 1/4 $A{B}^2$

$\Rightarrow$ AP $\times$AB = (1/4) $A{B}^2$

$\Rightarrow$ AP = 1/4 AB

Since, AB = 4cm

$\Rightarrow$ AP = 1/4 $\times$ (4cm)

$\Rightarrow$ AP = 1 cm