Question

Let ABCD be a circumscribed quadrilateral to a given circle. Show that circles inscribed in the two triangles ABC and ADC touch each other.​

Answer 1

Given:  ABCD be a circumscribed quadrilateral to a given circle.

To find: Show that circles inscribed in the two triangles ABC and ADC touch each other.

Solution:

• Now we have given that a quadrilateral ABCD is there, AC is joined.

• Let the circle inscribes in ABC be x1 and circle inscribes in ADC be x2.

• Let the point touching circle x1 and line AC be P and he point touching circle x2 and line AC be Q.

• Then:

                PQ = AQ - AP

                PQ = 1/2(AD+AC-DC) - 1/2(AB+AC-BC)

                PQ = 1/2(AD-DC-AB+BC) = 0

Answer:

               So the quadrilateral is circumscribed as PQ = 0.

Answer 2

Step-by-step explanation:

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