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
Answers
Answer:3v3 cm
Step-by-step explanation:
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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