Krishna
0

Step  1: Draw a imaginary diagram according to the question

NOTE: Since ABCD is a parallelogram,

AB = CD ..............(1)

Step 2: Mark the circle touching points with the sides of the parallelogram.

(S, P, Q, and R tangencies )

Step 3: Observe the figure and Write the equal lengths

NOTE: Lengths of tangents from an external points are equal.

EXAMPLE:    DR = DS (Tangents on the circle from point D)

CR = CQ (Tangents on the circle from point C)

BP = BQ (Tangents on the circle from point B)

AP = AS (Tangents on the circle from point A)

Step 4: Adding all these equations, (Obtained in step 3)

EXAMPLE: DR + CR + BP + AP = DS + CQ + BQ + AS

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

CD + AB = AD + BC

Step 5: Putting the values of equations (1) and (2) in the equation obtained in step 3, (See the step 1 for Eq (1)&(2))

EXAMPLE:      2AB = 2BC

AB = BC …......(3)

Step 6:  Compare equation 1, 2 and 3 (See step 1 and step  5)

NOTE: All the sides of the parallelogram are equal so, it is a rhombus

EXAMPLE: AB = BC = CD = DA

Hence, ABCD is a rhombus.