Two circles intersect each other at points P and Q If AB and AC are the tangents to the - Maths - Circles

Question

Two circles intersect each other at points P and Q If AB and AC
are the tangents to the circles from a point A on QP produced show
that AB=AC
Reply as fast as possible please

Priyanka Kedia · Accepted Answer

We know that,
If a tangent segment and a secant intersect in the exterior
of a circle, then the square of a length of the tangent segment is
equal to the product of the length of the secant segments and its
exterior part
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ana_qa_image_57b2e75d51640%20png">

Since AB is tangent and APQ is a secant Therefore,
AB2=AQ×AP 1
Similarly, AC is tangent and APQ is a secant So,
AC2=AQ×AP 2
From (1) and (2), we have,
AB2=AC2⇒AB=ACHence Proved

Two circles intersect each other at points P and Q. If AB and AC are the tangents to the circles from a point A on QP produced show that AB=AC Reply as fast as possible please

Two circles intersect each other at points P and Q. If AB and AC are the tangents to the circles from a point A on QP produced show that AB=AC

Reply as fast as possible please