Geometry - Study Mode

[#121] XYZ is a triangle. If the medians ZL and YM intersect each other at G, then (Area of ΔGLM : Area of ΔXYZ) is:
Correct Answer

(B) 1 : 12

Explanation

Solution: LM = YZ = 1 : 2 Area of ΔGLM : ΔGYZ = 1 : 4 ΔXYZ = 4 × 3 = 12 Area of ΔGLM : Area of ΔXYZ = 1 : 12

[#122] In a circle of radius 3 cm, two chords of length 2 cm and 3 cm lie on the same side of a diameter. What is the perpendicular distance between the two chords?
Correct Answer

(B) $$frac{{4sqrt 2 - 3sqrt 3 }}{2}{ ext{ cm}}$$

Explanation

Solution: $$eqalign{
& { ext{Radius of circle}} = 3 cr
& { ext{Length of chord }}AB = 3 cr
& { ext{Length of chord }}CD = 2 cr
& Rightarrow { ext{In, }}Delta OMB, cr
& OM = sqrt {{3^2} - {{left( {1.5}
ight)}^2}} cr
& = frac{3}{2}sqrt 3 cr
& Rightarrow { ext{In, }}Delta OND, cr
& ON = sqrt {{3^2} - {1^2}} cr
& = 2sqrt 2 cr
& x08ot { ext{ distance between two chords}} = ON - OM cr
& = frac{{2sqrt 2 }}{1} - frac{{3sqrt 3 }}{2} cr
& = frac{{4sqrt 2 - 3sqrt 3 }}{2} cr} $$

[#123] AD is perpendicular to the internal bisector of ∠ABC of ΔABC. DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm.) is
Correct Answer

(D) 6

Explanation

Solution: ∠ABD = ∠MBD = θ (angle bisector) ∴ SD ⊥ AM ∠BDA = ∠BDM = 90° It happen only in equilateral and isosceles triangle ∴ AD = DM i.e. AD = $$frac{{{ ext{AM}}}}{2}$$ Given DE || BC From Thales theorem E will be mid point of AC ∵ AC = 12 cm So, AE = 6 cm

[#124] In the given figure, ABCD is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP?
Correct Answer

(A) 4√5

Explanation

Solution: Let P is the mid point of AD $$eqalign{
& BP = sqrt {A{P^2} + A{B^2}} cr
& = sqrt {A{P^2} + 16} cr
& = sqrt {{2^2} + 16} cr
& = sqrt {20} cr
& { ext{Similarly }}CP = sqrt {20} cr
& BP + CP = sqrt {20} + sqrt {20} = 4sqrt 5 cr} $$

[#125] Select the correct option with respect to the given statement. Two tangents are drawn at the end of the diameter of a circle.
Correct Answer

(C) They are parallel to each other

Explanation

Solution: AB is the Diameter of the circle, and Tangents PQ and RS are parallel to each other.