To find angle BAD, we use the property that an angle at the centre of a circle is twice the angle at the circumference. Angle ODB is given as 25 degrees, making the angle at the centre (BOA) 50 degrees. Angle BAD is half of this, hence 20 degrees.

2022年4月6日 · The angle ODB is an angle formed between the radius OD and the tangent ED at point D. By the tangent-secant theorem, this angle (ODB) is equal to the angle formed at the circumference of the circle in the same segment, which is angle BAD.

To prove that angles ODB and ODC are right angles, we need to establish that each angle measures 90 degrees. This can be done using the properties of perpendicular lines or by using the concept of complementary angles.

【答案】 D【分析】 由SAS证明 AOC =ABOD得出∠OCA=∠ODB ,AC =BD ,O正确; 由全等三角形的性质得出∠OAC=∠OBD ,由三角形的外角性质得:∠AMB +∠OAC=∠AOB+∠OBD ,得出 ∠AMB =∠AOB =40° ,②正确; 作OG⊥MC于G ,OH⊥MB于H ,如图所示:则∠OGC =∠OHD =90° ,由AAS证明 OCG ODH (AAS),得出 OG =OH ,由角平分线的判定方法得出MO平分∠BMC ,正确; 由∠AOB =∠COD ，得出当∠DOM =∠AO M时，OM才平分∠BOC ，假设∠DOM =∠AOM ，由 AOC = …

2023年12月6日 · To find angle BAD, we first start with the given angle ODB, which is 25°. This angle, ODB, is formed between the radius OB and the tangent ED at point D. According to circle theorems, the angle at the center (angle AOB) is twice the angle at the circumference subtended by the same arc.

In the given figure O, is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26° find: a. Angle in semi-circle is a right angle. b. Sum of all angles in a triangle = 180°. d. In ΔODB, OB = OD ... (Radii of same circle) Tangent to a Circle. Is there an error in …

2023年12月17日 · (i) ∠BCD = ∠DAE = 70° (exterior angle of a cyclic quadrilateral is equal to opposite interior angle.) (ii) ∠BOD = 2∠BCD = 140° (angle subtended by an arc at the center is double the angle subtended by it on the remaining part on the circle.) (iii) In ΔBOD, OB = OD (radii) ∴ ∠OBD = ∠ODB = 180 – ∠BOD / 2 = 20°

Since OA and OC are both radii of the circle, angle OAC is equal to angle OBD because they subtend the same arc AB. Similarly, angle OCA is equal to angle ODB because they subtend the same arc CD. Therefore, by the Angle-Angle (AA) criterion for similarity, we conclude that triangle OCA is similar to triangle OBD.

【答案】a【解析】【分析】由题意易得∠aoc=∠bod，然后根据三角形全等的性质及角平分线的判定定理可进行求解．【详解】解：∵∠aob=∠cod=40°，∠aod是公共角，∴∠cod+∠aod=∠boa+∠aod，即∠aoc=∠bod，∵oa=ob，oc=od，∴ aoc≌ bod（sas），∴ac=bd，∠oac=∠obd，∠odb ...

Angle Sum of a Triangle: The sum of the angles in any triangle is 180 degrees. Using BD = OD: This given condition is crucial for finding the angles. Since OD is a radius, and BD = OD, triangle OBD is isosceles.