Question

9. In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three the sides are AB = 6 cm, BC =7 cm and CD = 4 cm. Find AD.​

Answer 1

Answer:

Hence, AD = 3 cm. In the given figure, a circle touches all the four side of quadrilateral ABCD with AB=6 cm, BC=7 cm and CD=4 cm.

Step-by-step explanation:

Let the circle touches the sides AB, BC, CD and DA at P, Q, R, S respectively

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

AP = AS —-(1) {tangents from A}

BP = BQ —(2) {tangents from B}

CR = CQ —(3) {tangents from C}

DR = DS—-(4) {tangents from D}

Adding (1), (2) and (3) we get

∴ AP + BP + CR + DR = AS + BQ + CQ + DS

⇒ (AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ)

⇒ AB + CD = AD + BC

⇒ AD = (AB + CD) – BC = {(6 + 4) – 7} cm = 3 cm

Hence, AD = 3 cm

Answer 2

Answer:

Hi friend.

I like to answer your question.

AS and AP are tangents drawn from A to the circle

⟹AS=AP

Similarly

DS=DR,RC=CQ,QB=BP

AB=AP+PB=6

AP=6−PB

BC=BQ+QC=7cm

CD=CR+DR=4cm

AD=AS+SD=AP+RD

=(6−PB)+(4−CR)

=10–(PB+CR)

=10–(BQ+CQ)=10−BC

=10–7

Ans:3cm