Question
Download Solution PDFIn ΔABC, AB = AC, O is the point on BC such that BO = CO and OD is perpendicular to AB and OE is perpendicular to AC. If ∠BOD = 60°, then measure of ∠AOE is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In ΔABC, AB = AC, O is the point on BC such that BO = CO and OD is perpendicular to AB and OE is perpendicular to AC.
∠BOD = 60°
Concept used:
1. In an isosceles triangle, we have one angle bisector that is also a median and an altitude.
2. All internal angles of a triangle sum up to 180°.
Calculation:
ΔOBD is a right-angled triangle at D and ∠BOD = 60°
So, ∠OBD = 90° - 60° = 30°
Since in ΔABC, AB = AC, ∠OBD = ∠ACB = ∠ABC = 30°
So, ∠BAC = 180° - 2 × 30° = 120°
Since BO = OC, AO is a median.
According to the concept,
∠BAO = ∠OAC = ∠OAE = 120/2 = 60°
Since OE is perpendicular to AC, ΔOEA is a right-angled triangle at E.
∠AOE = 90° - 60° = 30°
∴ The measure of ∠AOE is 30°.
Last updated on Jul 8, 2025
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