Question

in a circle points b p and q are points of contact of the respective tangent. line QA is parallel to line PC. if a is equal to 7.2 CM BC is equal to 5 cm find the radius of the circle

Answer 1

Answer:

Explanation:

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Answer 2

The radius of the circle is 6cm.

Given,

In a circle points B, P and Q are points of contact of the respective tangent. QA ║ PC.  AB = 7.2 cm and BC = 5 cm.

To find,

Radius of the circle.

Solution,

In ΔQOA and ΔBOA,

QA = AB   (Tangent segregates from external point)

OA = OA   (Common side)

OQ = OB   (Radii of the same circle)  

∴ ΔQOA ≅ ΔBOA   (SSS rule)

⇒∠QOA = ∠BOA    (CPCT)

Let ∠QOA = ∠BOA = x                   -(1)

In ΔBOC and ΔPOC,

OC = OC   (Common side)

OP = OB    (Radii of the same circle)

PC = BC   (Tangent segregates from external point)

∴ ΔBOC ≅ ΔPOC   (SSS rule)

⇒∠BOC = ∠POC    (CPCT)

Let ∠BOC = ∠POC = y                   -(2)

∠QOA + ∠BOA + ∠BOC + ∠POC = 180°  (Linear pair)

x + x + y + y = 180°

2(x + y) = 180°

x + y = 90°

⇒ ∠BOA + ∠BOC = 90°           (from 1 and 2)

∴∠AOC = 90°

In ΔAOC,

∠AOC = 90°

OB ⊥ AC

∴ By theorem of geometric mean,

OB² = AB x BC

OB² = 7.2 x 5              (AB = QA; BC = PC)

OB² = 36

OB = √36

OB = 6cm

∴Radius of the circle is 6cm.

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