Question

PQ and XY are two chords of a circle
such that PQ = 6 cm and XY = 12 cm
and PQ||XY. If the distance between
the chords is 3 cm then the radius of
the circle is
(a) 3V3 cm (b) 3V5 cm
(c) 573 cm
(d) 5 cm​

Answer 1

Answer:3v3 cm

Step-by-step explanation:

Answer 2

Given :- (from image.)

• XY chord = 12 cm. => Z bisects the chord.
• PQ chord = 6cm . => R bisects the chord.
• radius = OX = OP = r cm.
• ZR = distance between chord = 3 cm.
• OZ = Let x cm.
• OZ ⟂ XY.
• OR ⟂ PQ

Solution :-

in Right ∆OXZ ,

→ OX² = OZ² + XZ²

→ r² = x² + 6²

→ r² = (x² + 36) ------------ Eqn.(1)

in Right ∆ORP ,

→ OP² = (OZ + ZR)² + PR²

→ r² = (x + 3)² + 3² --------- Eqn.(2)

from Eqn.(1) and Eqn.(2) equating the value of r² ,

→ (x + 3)² + 3² = x² + 36

→ x² + 6x + 9 + 9 = x² + 36

→ 6x + 18 = 36

→ 6x = 36 - 18

→ 6x = 18

→ x = 3 cm

Putting value of x in Eqn.(1), we get

→ r² = 3² + 36

→ r² = 45

→ r = √45

→ r = 3√5 cm. (Ans.)

Hence, the radius of the circle is 3√5 cm.

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