In the adjacent figure if PA = 4 cm, BP = 3 cm and AC = 11 cm then BC

1.	In the adjacent figure if PA = 4 cm, BP = 3 cm and AC = 11 cm then BC =(A) 15 cm (B) 14 cm (C) 7 cm (D) 10 cm
Answer» Correct option is: (D) 10 cm \(\because\) Tangents drawn from a fixed outer point to circle are of equal length. \(\therefore\) AP = AR, (Tangents drawn from outer point A) BP = BQ, (Tangents drawn from outer point B) and CQ = CR, (Tangents drawn from outer point C) Now, BC = BQ + QC = BP + CR (\(\because\) BQ = BP and QC = CR) = 3 + AC - AR (\(\because\) BP = 3cm (Given) & CR = AC - AR) = 3 + 11 - PA (\(\because\) AC = 11 cm (given) & AR = AP = PA) = 14 - 4 (\(\because\) PA = 4 cm (given)) = 10 cm. Correct option is: (D) 10 cm

In the adjacent figure if PA = 4 cm, BP = 3 cm and AC = 11 cm then BC =(A) 15 cm (B) 14 cm (C) 7 cm (D) 10 cm

Answer»

Correct option is: (D) 10 cm

\(\because\) Tangents drawn from a fixed outer point to circle are of equal length.

\(\therefore\) AP = AR, (Tangents drawn from outer point A)

BP = BQ, (Tangents drawn from outer point B)

and CQ = CR, (Tangents drawn from outer point C)

Now, BC = BQ + QC

= BP + CR (\(\because\) BQ = BP and QC = CR)

= 3 + AC - AR (\(\because\) BP = 3cm (Given) & CR = AC - AR)

= 3 + 11 - PA (\(\because\) AC = 11 cm (given) & AR = AP = PA)

= 14 - 4 (\(\because\) PA = 4 cm (given))

= 10 cm.

Correct option is: (D) 10 cm

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