Geometry - Study Mode

[#81] Each of the circles of equal radii with centres A and B pass through the centre of one another. They cut at C and D then ∠DBC is equal to?
Correct Answer

(C) 120°

Explanation

Solution: According to question AB = AD = DB = r ∴ ΔADB is a equilateral triangle ∠DBA = 60° Similar in ΔABC ∠ABC = 60° ∠DBC = 60° + 60° ∴ ∠DBC = 120°

[#82] In ΔABC, D is a point on BC such that ∠ADB = 2∠DAC, ∠BAC = 70° and ∠B = 56°. What is the measure of ∠ADC?
Correct Answer

(D) 72°

Explanation

Solution: Let ∠DAC = x ∠ADB = 2x ∠ACD + ∠DAC = ∠ADB ∠ACD + x = 2x ∠ACD = 2x - x = x In ΔABC ∠A + ∠B + ∠C = 180° 70° + 56° + ∠C = 180° ∠C = 54° ∠ADC = 180° - 2x = 180° - 2 × 54° = 180° - 108° = 72°

[#83] A cyclic quadrilateral ABCD is drawn in a circle with centre O. A and C are joined to O. If ∠ABC = 2p and ∠ADC = 3p, what is the measure (in degrees) of the ∠AOC reflex?
Correct Answer

(D) 206

Explanation

Solution: ABCD is cyclic quadrilateral ∴ 3p + 2p = 180° 5p = 180° p = 36° ∠ADC = 3p = 3 × 36 = 108° ∠AOC = $$frac{1}{2}$$∠ADC = $$frac{1}{2}$$ × 108° = 54° Reflex of ∠AOC = 360° - 54° = 206°

[#84] ln ΔABC, D is a point on side BC such that ∠ADC = 2∠BAD. If ∠A = 80° and ∠C = 38°, then what is the measure of ∠ADB?
Correct Answer

(D) 56°

Explanation

Solution: ∠ADB = 180° - 62° - 62° = 56°

[#85] Which of the following is a true statement
Correct Answer

(C) Two triangle are similar if their corresponding sides are proportional

Explanation

Solution: Two triangles are similar if their corresponding sides are proportional.