The perimeter of right-angle triangle is 60 cm and its hypotenuse is 26 cm. What is the area (in cm2) of the triangle?
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In an isosceles ΔABC, AD is the median to the unequal side meeting BC at D. DP is the angle bisector of ∠ADB and PQ is drawn parallel to BC meeting AC at Q. Then the measure of ∠PDQ is
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Two concentric circles are of redii 13 cm and 5 cm. The length of the chord of the larger circle
which touches the smaller circle is:
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Two tangents AP and AQ are drawn to a circle with centre O from an external point A, where P and Q are points on the circle. If AP = 12 cm and ∠PAQ = 60°, then the length of chord PQ is:
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Two tangents PA and PB are drawn from an external point P to a circle with centre O at the points A and B respectively on it, such that ∠APB = 120° and AP = 12.5 cm. The length of OP is:
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In the given figure, PT is a common tangent to three circles at points A, B and C respectively. The radius of the small, medium and large circles is 4 cm, 6 cm and 9 cm. O1, O2 and O3 are the centre of the three circles what is the value (in cm) of PC?
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In ΔPQR, S is a point on the side QR such that ∠QPS = ∠PSR, ∠QPR = 78° and ∠PRS = 44°. What is the measure of ∠PSQ?
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A secant is drawn from a point P to a circle so that it meets the circle first at A, then goes through the centre, and leaves the circle at B. If the length of the tangent from P to the circle is 12 cm, and the radius of the circle is 5 cm, then the distance from P to A is:
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In ΔABC, D and E are points on the sides AB and AC, respectively, such that DE || BC and DE : BC = 6 : 7. (Area of ΔADE) : (Area of trapezium BCED) = ?
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In the given figure, ABCD is a rectangle and P is a point on DC such that BC = 24 cm, DP = 10 cm and CD = 15 cm. If AP produced intersects BC produced at Q, then the length of AQ.
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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).
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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:
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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 . then the radius of the circle is:
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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, is equal to:
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In the given figure, PQRS is a cyclic quadrilateral. What is the measure of the angle PQR if PQ is parallel to SR?
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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 ?
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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:
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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:
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In the following figure, AD bisects angle BAC. Find the length (in cm) of BD.
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In the given figure, if and PY = 18 cm, then what is the value (in cm) of PQ?
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