61.
An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the side AB and AC respectively of ΔABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, sin 75° = ?

62.
In a triangle ABC, the side BC is extended up to D such that CD = AC. If ∠BAD = 109° and ∠ACB = 72° then the value of ∠ABC is

63.
The equidistant point from the vertices of a triangle is called its:

64.
Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is

65.
ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to

66.
The sum of three altitudes of a triangle is

67.
In ΔABC, ∠B = 60° and ∠C = 40°. If AD and AE be respectively the internal bisector of ∠A and perpendicular on BC, then the measure of ∠DAE is

68.
In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e., hypotenuse. One of the acute angle must be

69.
In a ΔABC ∠A : ∠B : ∠C = 2 : 3 : 4. A line CD drawn || to AB, then the ∠ACD is :

70.
BL and CM are medians of ΔABC right-angled at A and BC = 5 cm. If BL = $$\frac{{3\sqrt 5 }}{2}$$ cm, then the length of CM is

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