In the given figure ab and BC are two chords of a circle whose Centre is O such that angle abc is equal to angle CBD if a b is equals to 6 cm and angle b is equal to 30 degree find the measure of BC and angle AOC
Answers
Measure of BC = 6 cm and m∠AOC = 60°
Step-by-step explanation:
Given data:
∠ABC = 30° and AB = 6 cm
∠ABO = ∠CBO
We know that, angle subtended by the arc at the centre is twice the angle subtended by it at any point on the remain part of the circle.
⇒ m∠AOC = 2 m∠ABC
⇒ m∠AOC = 2 × 30°
⇒ m∠AOC = 60°
Construction: Draw a perpendicular line from centre to chord AC which meets it at M.
In ΔABM and ΔCBM,
AM = CM (Perpendicular from centre to chord bisects the chord)
∠BMA = ∠BMC (Each 90°)
BM = BM (common)
∴ ΔABM ≅ ΔCBM by SAS congruence rule.
By CPCT,
AB = BC
BC = 6 cm
Hence BC = 6 cm and m∠AOC = 60°.
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