Geometry - Study Mode

[#156] If M is the mid-point of the side BC of ΔABC, and the area of ΔABM is 18 cm 2 , then the area of ΔABC is:
Correct Answer

(C) 36 cm 2

Explanation

Solution: BM : MC= 1 : 1 Area of ΔBMA : Area of ΔAMC = 1 : 1 ↓ 18 2 unit → 18 × 2 Area of ΔABC = 36 cm 2

[#157] In the given figure, PQ = PS = SR and ∠QPS = 40°, then what is the value of ∠QPR (in degrees)?
Correct Answer

(C) 75

Explanation

Solution: ∠PQS = ∠PSQ = $$frac{{{{180}^ circ } - {{40}^ circ }}}{2}$$ xa0 = 70° ∠PSR = 180° - 70° = 110° ∠SPR = ∠SRP = $$frac{{{{180}^ circ } - {{110}^ circ }}}{2}$$ xa0 = 35° ∠QPR = ∠QPS + ∠SPR = 40° + 35° = 75°

[#158] ABC is an equilateral triangle. Points D, E and F are taken as the mid-point on sides AB, BC, CA respectively, so that AD = BE = CF. Then AE, BF, CD enclosed a triangle which is:
Correct Answer

(A) equilateral

Explanation

Solution: Given in question AD = BE = CF [DB = AF = EC] Because AB = BC = CA So, Triangle is equilateral

[#159] Incentre of ΔABC is I. ∠ABC = 90° and ∠ACB = 70°. Then ∠BIC is
Correct Answer

(B) 100°

Explanation

Solution: ∵ Sum of all angles of a triangle = 180° So, ∠BAC = 180° - (90° + 70°) = 20° So, ∠BIC = 90° + $$frac{1}{2}$$∠A ∠BIC = 90° + $$frac{1}{2}$$ × 20° ∠BIC = 100°

[#160] In ΔABC, the bisector of ∠A intersect side BC at D. If AB = 12 cm, AC = 15 cm and BC = 18 cm, then the length of BD is:
Correct Answer

(B) 8 cm

Explanation

Solution: BD : DC = 12 : 15 = 4 : 5 BD = 18 × $$frac{4}{9}$$ = 8 cm