Question

ABCD IS CIRCUMSCRIBED QUADRILATERAL WITH AB=4,BC=5,CD=3 THEN FIND AD=?

Answer 1

ABCD is a quadrilateral. A circle touches the sides AB, BC, CD and DA of the quadrilateral ABCD at P, Q, R and S respectively

.AB = 6 cm, CD = 4 cm and BC = 7 cm

We know that, the length of tangents drawn from an external point to the circle are equal.

AP = AS

BP = BQ

CQ = CR

DR = DS

Now, AB + CD = (AP + PB) + (CR + DR)

= (AS + BQ) + (CQ + DS)

= (AS + DS) + (BQ + CQ)

= AD + BC

∴ AB + CD = AD + BC

⇒ AD = AB + CD – BC

⇒ AD = 6 cm + 4 cm – 7 cm

⇒ AD = 10 cm – 7 cm

⇒ AD = 3 cm

Thus, the length of the side AD is 3 cm.

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Answer 2

Answer:

We know that when a quadrilateral circumscribes a circle then sum of opposes sides is equal to the sum of other opposite sides
therefore ab + dc = ad + bc

so ad = 2