Question

In the figure, AB is a tangent to the circle with center O1 and AC is a tangent to the circle with center O2 AD is a common tangent. Prove that AB=AC. ​

Answer 1

$\huge\star\underline\mathfrak\green{Answer:-}$

From the given figure, AB and CD are common tangents on both the circles. AB and CD intersect at E.

Now, EA=EC (Tangents drawn on circle from same point)

EB=ED (Tangents drawn on circle from same point)

EA+EB=EC+ED

AB=CD