The diameter AC and the chord BD intersecting at the point M are drawn in a circle with center O
| August 14, 2021 | education
The diameter AC and the chord BD intersecting at the point M are drawn in a circle with center O, and BM = DM. BAC angle = 35 degrees. Find the corner BAD
We connect points B and D with the center of the circle O.
ΔОВМ = ΔОDM.
<OMB = <OMD (both adjacent to the OM).
Sum of adjacent angles: <OMB + <OMD = 180 °.
Each of these angles is 90 °.
(It is proved that if the diameter divides the chord in half, then the chord and the diameter are mutually perpendicular).
Two right-angled triangles – AVM and AMB – have a common leg AM. The other two corresponding legs are equal by the condition: BM = MD.
Therefore, ΔАВМ = ΔАМB, and <BAM = <MAD = 35 °.
<BAD = <BAM + <MAD = 35 ° + 35 ° = 70 °.
Answer: 70 °.
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