# Q1) From an external point P, tangents PA and PB are drawn to a circle with cente O.If CD is the tangent to the circle at a point E and PA=14cm, find the perimeter of triangle PCD.Q2) a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB=6cm, BC=7cm, and CD=4cm find AD.if possible u pls. explain me these sums through video.

PA and PB are tangent to the circle with centre O. CD is a tangent to the circle at E, which intersect PA and PB in C and D respectively.

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

∴ PA = PB

CA = CE

DB = DE

PA = PB = 14 cm  (Given)

Perimeter of ΔPCD = PC + CD + PD

= PC + (CE + ED) + PD

= PC + (CA + DB) + PD

= (PC + CA) + (DB + PD)            ( CA = CE and DB = DE)

= PA + PB

= 14 cm + 14 cm

= 28 cm

∴ Perimeter of ΔPCD = 20 cm

2.

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)

AB + CD = AD + BC

⇒ AD = AB + CD – BC

⇒ AD = 6 cm + 4 cm – 7 cm

⇒ AD = 10 cm – 7 cm

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

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