Question

Match the following:

• A. AP + DR = 5 cm
• B. DC = 7 cm
• C. DC = 9 cm

Answer 1

(i) - By Theorem- For quadrilateral circumscribing circle
AB + DC = AD + BC
$\therefore$ 6 + DC = 5 + 8
$\Rightarrow$ DC = 7 cm

(ii) - By Theorem- Tangents from external point are equal in lengths
$\therefore$ DR = DQ = 7 cm
and, CR = CP = 2 cm
$\because$ DC = DR + CR
$\therefore$ DC = 7 + 2 = 9 cm

(iii) By Theorem- Tangents from an external point are equal in lengths
$\therefore$ CR = CQ = 4 cm
and BQ = BP = 2 cm

Now, AB = AP + BP = AP + 2,
DC = DR + CR = DR + 4
and, BC = BQ + CQ = 2 + 4
By Theorem- For quadrilateral circumscribing circle
AB + DC = AD + BC
$\therefore$ (AP + 2) + (DR + 4) = 5 + (2 + 4)
$\Rightarrow$ AP + DR = 5 cm