71. In a right triangle ABC, right angled at B, altitude BD is drawn to the hypotenuse AC of the triangle. If AD = 6 cm, CD = 5 cm, then find the value of AB2 + BD2 (in cm).
72. In the given figure, TB is a chord which passes through the centre of the circle. PT is a tangent to the circle at the point T on the circle. If PT = 10 cm, PA = 5 cm and AB = x cm, then the radius of the circle is:
73. A square is inscribed in a quarter-circle in such a manner that two of its adjacent vertices lie on the two radii at an equal distance from the centre, while the other two vertices lie on the circular arc. If the square has sides of length $$x$$. then the radius of the circle is:
74. In ΔABC, ∠C = 90°, point P and Q are on the sides AC and BC, respectively, such that AP : PC = BQ : QC = 1 : 2. Then, $$\frac{{{\text{A}}{{\text{Q}}^2} + {\text{B}}{{\text{P}}^2}}}{{{\text{A}}{{\text{B}}^2}}}$$ is equal to:
75. In the given figure, PQRS is a cyclic quadrilateral. What is the measure of the angle PQR if PQ is parallel to SR?
76. AB is a diameter of the circle with centre O, CD is chord of the circle, If ∠BOC = 120°, then the value of ∠ADC is ?
77. PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that ∠APB = 142°, then ∠OAB is equal to:
78. 
A circle is inscribed in the triangle ABC whose sides are given as AB = 10, BC = 8, CA = 12 units as shown in the figure. The value of AD × BF is:
A circle is inscribed in the triangle ABC whose sides are given as AB = 10, BC = 8, CA = 12 units as shown in the figure. The value of AD × BF is:
79. In the following figure, AD bisects angle BAC. Find the length (in cm) of BD.
80. In the given figure, if $$\frac{{{\text{QR}}}}{{{\text{XY}}}} = \frac{{14}}{9}$$ and PY = 18 cm, then what is the value (in cm) of PQ?
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