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)
= 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.