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Class 9 Maths Study Material and NCERT Solutions Get Free NCERT Solutions for Class 10 Maths Chapter 9 Ex PDF. Some Applications of Trigonometry Class 10 Maths NCERT Solutions are extremely helpful while doing your homework or while preparing for the exam. Exercise Class 10 Maths NCERT Solutions were prepared according to CBSE marking scheme and guidelines. Nov 27, �� Theorem The tangent at any point of a circle is perpendicular to the radius through the point of contact. Given: A circle with center O. With tan.
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Solution: The angle subtended by an arc of a circle at its centre is twice the angle subtended by the same arc at a point pn the circumference. In figure, A, B and C are four points on a circle. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. Solution: Since angles in the same segment of a circle are equal.

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle. If the non � parallel sides of a trapezium are equal, prove that it is cyclic.

Two circles intersect at two points B and C. Solution: Since, angles in the same segment of a circle are equal. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side. They intersect at a point D, other than A. Let us join A and D. Thus, D lies on BC.

Case � I: If both the triangles are in the same semi-circle. Join BD. DC is a chord. Case � II : If both the triangles are not in the same semi-circle. Prove that a cyclic parallelogram is a rectangle. Since, ABCD is a cyclic quadrilateral. Thus, ABCD is a rectangle. Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

Two chords AB and CD of lengths 5 cm and 11 cm, respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle. Solution: We have a circle with centre O. Let r cm be the radius of the circle. The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

Parallel chords AB and CD are such that the smaller chord is 4 cm away from the centre. Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Proof: An exterior angle of a triangle is equal to the sum of interior opposite angles. Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals. Taking AB as diameter, a circle is drawn.

A circle drawn with Q as centre, will pass through A, B and O. ABCD is a parallelogram. ABCE is a cyclic quadrilateral. AC and BD are chords of a circle which bisect each other. Similarly, AC is a diameter. Since, opposite angles of a parallelogram are equal.

Two congruent circles intersect each other at points A and B. Solution: We have two congruent circles such that they intersect each other at A and B. A line segment passing through A, meets the circles at P and Q. What should be the length of the slide in each case? Find the height of the tower. A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground.

Find the length of the string, assuming that there is no slack in the string. Find the distance he walked towards the building. A statue, 1. Find the height of the pedestal. If the tower is 50 m high, find the height of the building. Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide.

Find the height of the poles and the distance of the point from the poles. A TV tower stands vertically on a bank of a canal.

Find the height of the tower and the width of the CD and 20 m from pole AB. Determine the height of the tower. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. Find the distance travelled by the balloon during the interval. A straight highway leads to the foot of a tower. Find the time taken by the car to reach the foot of the tower from this point.

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

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