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प्रश्न
In the above figure, m(arc DXE) = 105°, m(Arc AYC) = 47°, then find the measure of ∠DBE.
बेरीज
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उत्तर
Chord AD and CE intersect externally at point B.
When two secants (or chords extended) intersect outside a circle, the measure of the angle formed is half the difference of the measures of the intercepted arcs.
∴ m∠DBE = `1/2["m"("arc" "DXE") - "m"("arc" "AYC")]`
∴ m∠DBE = `1/2 [105^circ - 47^circ]`
∴ m∠DBE = `1/2[58^circ]`
∴ m(∠DBE) = 29°
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