Question
Download Solution PDFIn a circle with centre O. AB is the diameter and CD is a chord such that ABCD is a trapezium. If ∠BAC = 25°, then ∠CAD is equal to∶
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven, ∠BAC = 25°
⇒ ∠ACB = 90° [Angle in a semicircle is 90]
In ΔACB
⇒ ∠ACB + ∠CBA + ∠BAC = 180°
⇒ ∠CBA = 180° – 90° – 25° = 65°
⇒ ∠DCA = ∠CAB = 25° [Alternate interior angle]
⇒ ∠DCA = ∠ABD = 25°and ∠CAD = ∠DBC
∵ Two inscribed angles forming the same arc or forming two equal arcs are equal.
⇒ ∠CBA = ∠DBC + ∠ABD
⇒ 65° = ∠DBC + 25°
⇒ ∠DBC = 65° – 25° = 40°
⇒ ∠CAD = ∠DBC = 40°
Last updated on Jun 13, 2025
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