71. A is a point at a distance 26 cm from the centre O of a circle of radius 10 cm. AP and AQ are the tangents to the circle at the point of contacts P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B, AQ at C, then the perimeter of ΔABC is:
72. In a circle, PQ and RS are two diameters that are perpendicular to each other. Find the length of the chord PR.
73. Let AX ⊥ BC of an equilateral triangle ABC. Then the sum of the perpendicular distances of the sides of ΔABC from any point inside the triangle is:
74. In the figure below, AB is a chord of a circle with centre O. A tangent AT is drawn at point A so that ∠BAT = 50°. Then ∠ADB = ?
75. Two circles with the same centre P have radii 7.5 cm and 4.4 cm. Through a point A of the larger circle, a tangent is drawn to the smaller circle touching it at B. Find AC (Approximate in cm).
76. In ΔABC, E and D are points on sides AB and AC, respectively, such that ∠ABC = ∠ADE. If AE = 6 cm, AD = 4 cm and EB = 4 cm, then the length of DC is:
77. A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm and PB = 22.5 cm, then the radius of the circle is:
78. In the given, figure, CD and AB are diameters of circle and AB and CD are perpendicular to each other, LQ and SR are perpendiculars to AB and CD respectively. Radius of circle is 5 cm, PB : PA = 2 : 3. What is the length (in cm) of SM?
79. In the following figure (not to scale), at the centre O, if the chord AB students double the angle that is subtended by chord CD and the angle ∠AEB = 2∠AOB, then ∠COD is equal to:
80. A circle inscribed in a triangle ABC touches its sides AB, BC and AC at the points D, E and F, respectively. If AB = 18 cm, BC = 15 cm and AC = 13 cm, then the value of AD + BE + CF is:
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