Question

In the given figure PAQ is the tangent of the circle at point A and ABCD is a cyclic quadrilateral. If angle CAQ =70 Than angleABC?

Answer 1

Answer

<ABC = 70°

Explanation

See the attachment with the answer

In the given information,

PAQ is the tangent of the circle at point A and ABCD is a cyclic quadrilateral.

If angle CAQ =70  we get AC is a chord and <CAQ is the angle made by CA and tangent at A

<ABC is the angle made by same chord.

Therefore <ABC = < CAQ = 70°

Answer 2

Given ABCD is a cyclic quadrilateral  

At point A PAQ is a tangent to the circle.

We know angle CAQ = 70. Here angle made by CA is the angle CAQ and is tve tangent at A.

                AC is a chord

<ABC is the angle made by same chord.  

Therefore <ABC is equal to < CAQ = 70°

We can also write this as  

Given ABCD is a quadrilateral.

Also angle CAQ = 70 degree

PAQ is the tangent of circle at A. This will be CA.

Now CA is the chord of the circle.

CAQ = 70 degree and so angle ABC = 70 degree