Question

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

Answer 1

Answer:

Answer

5 cm

Solution

Construction: Mark the touchi ng points to the circle as P, Q R and S as Shown in the figure.(above attachment)

As we already know that tangents drawn from an external point to a circle are equal

Rightarrow AQ=AR=a

Rightarrow BR=BS=b

Rightarrow CP=CS=c Rightarrow DP=DQ=d

From the figure drawn above

⇒BC = BS + SC ⇒7=b+c(BC = 7cm)

⇒b=7-c... (i)

Also,

⇒ DC DP + PC

⇒ 4 = d+ c(DC = 4 cm)

⇒c=4-d... (ii)

And,

⇒ AB = AR + RB

⇒ 6 = a + b(AB = 6 cm)

⇒a=6-b... (iii) Using equation (1)

⇒a=6 (7- c)

Using equation (ii)

⇒a=6 (7-4+d) ⇒a= 6-7+4-d

⇒a=6 (7-(4-d)) . AD = 3 cm

⇒a+d=3

⇒ AQ+QD = 3

From the figure above, AQ+QD = AD

Hence, the length of AD is 3 cm.

Step-by-step explanation:

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Answer 2

Answer:

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