The distance between C and B along a straight line is 36 metres Town F is 50 km east of town G. The distance from F to H is 65 km. The diagram should show the c The ship leaves Port T and travels due west i north direction to a point X which is due north of R. The diagram below shows a map of Baytime drawn on a grid of 1 cm squares. The distance RT is 75 km and the distance RS is 56 km.
Show on your diagram a Find the nearest km, the shortest distance i the North direction between Rose Hall and South Port. The base, N, of an antenna rests on a horizontal ground.
N is Points O, P and Q are in the same horizontal plane. P is 15 m away from O on a bearing c A third point, C, lies on the ground 5. R is x degrees. Calculate to the nearest degree, the value of x. Clearly indicate North on your Q, R and S three points on a level ground.
S diagram. Q, R and S are three points on level ground. Runners draw a carefully labelled diagram to are to start at K and run 4 1cm due north to a represent the journey of the ship. The diagram above, not drawn to scale, shows a pole TF, 12 m high, standing on i the points K, L and M level ground. The points A, F and B lie in the same horizontal plane. In the diagram below, not drawn to scale, O i angle MCD is the centre of the circle. The diagram below, not drawn to scale, Calculate, giving your answer correct to 2 shows a circle, centre O, radius 15 cm.
The decimal places: length of the minor arc LM is 9 cm and LN is a tangent to the circle. OMN is a straight a the radius of the circle line. In the diagram, not drawn to scale, O is the b Determine the area, in cm2, of centre of the circle. In the diagram below, not drawn to scale, 9. AEC is a straight line through the centre centre O. SVT is a In the diagram below, not drawn to scale, O The diagram below, not drawn to scale, shows a circle, centre O. AC and BT are diameters. Calculate, giving reasons for your answers, the sizes of angles: Given a circle, centre 0 and radius 5 cm.
Tangents QT and QS are drawn from a point In the figure above, not drawn to scale, SR is Q to touch the circle at T and at 5. Angle a tangent to the circle. MP intersect at Q. Calculate the size of angle TRS. In the figure below, not drawn to scale, PQR is a circle with centre, O.
PO is parallel to QR. ABCT, inscribed in a circle. ED is a tangent to the circle at T. Calculate, giving reasons to support your answers, the size, in degrees, of the angles:.
Calculate, giving reasons for your answers, the AC and BD cut at F. Open navigation menu. Close suggestions Search Search. User Settings. Skip carousel. Carousel Previous. Carousel Next. What is Scribd? Explore Ebooks. Bestsellers Editors' Picks All Ebooks. Explore Audiobooks.
Bestsellers Editors' Picks All audiobooks. Explore Magazines. Editors' Picks All magazines. Explore Podcasts All podcasts. Difficulty Beginner Intermediate Advanced. Explore Documents. Trigonometry II and Circle Theorem. Uploaded by Anthony Benson. Document Information click to expand document information Original Title Did you find this document useful? Is this content inappropriate? Report this Document. Flag for inappropriate content.
Download now. Save Save Original Title: Related titles. Carousel Previous Carousel Next. Jump to Page. Search inside document. Circle review 2. Solution: Let x m be the distance of the object from the base of the cliff. Examples: 1. Solution: Solution: Let the height of the tree be h. Sketch a diagram to represent the situation.
Example: 1. Circle Theorems 1. Z is due east of Y. Calculate, giving your answers to 2 decimal places: a the area of triangle OAB b the area of the shaded region. Documents Similar To Roger Khan. Adarsh Dongare. Terry Kim. In a circle, a diameter bisects a chord and an arc with the same endpoints if and only if it is perpendicular to the chord.
If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc or the measure of the intercepted arc is twice the measure of the inscribed angle. If two inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent.
If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle. If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
If a line is perpendicular to a radius of a circle at its endpoint that is on the circle, then the line is tangent to the circle.
If two segments from the same exterior point are tangent to a circle, then the two segments are congruent. If two secants intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
If a secant and a tangent intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. If two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
If two secants intersect in the interior of a circle, then the measure of an angle formed is one-half the sum of the measures of the arcs intercepted by the angle and its vertical angle. If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of its intercepted arc.
If two chords of a circle intersect, then the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other chord. If two secant segments are drawn to a circle from an exterior point, then the product of the lengths of one secant segment and its external secant segment is equal to the product of the lengths of the other secant segment and its external secant segment. If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external secant segment.
Trees, Maps, And Theorems December
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