Question 17

All sides of a quadrilateral ABCD touch a circle. If AB = 6 cm. BC = 7.5 cm. CD = 3 cm, then DA is

Solution

Given : AB = 6 cm. BC = 7.5 cm. CD = 3 cm

To find : DA = ?

Solution : Tangents from the same point to a circle are equal in length.

=> $$AE=AH$$, $$BE=BF$$, $$CG=CF$$ and $$DG=DH$$

Adding above equations, we get :

=> $$(AE+BE)+(CG+DG)=(BF+CF)+(AH+DH)$$

=> $$AB+CD=BC+DA$$

=> $$6+3=7.5+DA$$

=> $$DA=9-7.5=1.5$$ cm

=> Ans - (D)

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