In fig. a circle touches all the four sides of quadrilateral ABCD with AB = 6cm, BC = 7cm, CD = 4cm. Find AD.
We know that the tangents drawn from any external point to circle are equal in length.
From A ⟶ AS = AP ….(i)
From B ⟶ QB = BP …. (ii)
From C ⟶ QC = RC …..(iii)
From D ⟶ DS = DR …. (iv)
Adding (i), (ii), (iii) & (iv)
(AS + QB + QC + DS) = (AB + BP + RC + OR)
(AS + DS) + (QB + QC) = (AP + BP) + (RC + DR)
AD + BC = AB + CD
⇒ AD + 7 = 6 + 4 AD = 3cm
⇒ AD = 10 – 7 = 3cm
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