Question
Download Solution PDFAB is the diameter of a circle with centre O. C and D are two points on the circle on either side of AB, such that ∠CAB = 52° and ∠ABD = 47°. What is the difference (in degrees) between the measures of ∠CAD and ∠CBD?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
∠CAB = 52° and ∠ABD = 47°
Concept used:
The angle subtended by the diameter at any point on the circumference is equal to 90°
Calculation:
According to the concept,
∠ACB = ∠ADB = 90°
So, ∠CBA = 180° - (90° + 52°)
⇒ 180° - 142°
⇒ 38°
Similarly,
∠BAD = 180° - (90° + 47°)
⇒ 180° - 137°
⇒ 43°
So, ∠CAD = 52° + 43°
⇒ 95°
∠CBD = 38° + 47°
⇒ 85°
Now,
∠CAD - ∠CBD = 95° - 85°
⇒ 10°
∴ The difference (in degrees) between the measures of ∠CAD and ∠CBD is 10.
Last updated on Jul 12, 2025
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