In the given figure, 0 is the centre of the circle and ∠DCE = 45°. If CD = $$10\sqrt2$$ cm, then what is the length (in cm) of AC . CB = BD<img src="https://cracku.in/media/uploads/blob

1. In the given figure, 0 is the centre of the circle and ∠DCE = 45°. If CD = $$10\sqrt2$$ cm, then what is the length (in cm) of AC . CB = BD

Write Comment

Comments

By: anil on 05 May 2019 02.55 pm

Given : CD = $$10sqrt2$$ cm and BC = BD = $5sqrt2$$ => ∠OBC = 90° Also, ∠DCE = 45°, => ∠OCB = 45°, => OB = BC ---------(i) Now, in $$ riangle$$ OBC, => $$(OC)^2=(OB)^2+(BC)^2$$ => $$(OC)^2=(5sqrt2)^2+(5sqrt2)^2$$
=> $$(OC)^2=50+50=100$$ => $$OC=sqrt{100}=10$$ cm Similarly, in $$ riangle$$ ABC, => $$(AC)^2=(AB)^2+(BC)^2$$ => $$(AC)^2=(10+5sqrt2)^2+(5sqrt2)^2$$ => $$(AC)^2=100+50+100sqrt2+50$$ => $$(AC)^2=100(2+sqrt2)=341.42$$ => $$AC=sqrt{341.42}=18.47approx18.5$$ cm => Ans - (C)

Tags

Show Similar Question And Answers

QA->A cyclist goes 40 km towards East and then turning to right he goes 40 km. Again he turn to his left and goes 20 km. After this he turns to his left and goes 40 km, then again turns right and goes 10km. How far is he from his starting point?....

QA->On November 30, 2014, the Simon Wiesenthal Center reported that a senior Nazi figure who centrally involved in the implementation of the Holocaust had died in Syria around 2010, or four years earlier. Who is that Nazi figure?....

QA->Jose travels 7 km to the north.Then again he turns to the right and walks 3 km.Then again he turns to his right and moves 7 km forward.How many kilometers away is he from the starting point?....

QA->From a given point, how many tangents can be drawn to a circle?....

QA->A train of length 150 meters took 8 seconds to cross a bridge of length 250 meters. Time taken by the train to cross a telephone post is :....

MCQ->In the given figure, 0 is the centre of the circle and ∠DCE = 45°. If CD = $$10\sqrt2$$ cm, then what is the length (in cm) of AC . CB = BD

....

MCQ->If $$x=\frac{\sqrt2+1}{\sqrt2-1}$$ and $$y=\frac{\sqrt2-1}{\sqrt2+1}$$, then what is the value of x+y ? ....

MCQ-> Study the following information carefully and answer the questions given below:Eight friends P, Q, R, S, W, X, Y and Z are sitting around a circular table but not necessarily in the same order. Some of them are facing the centre and some others are facing outside (i.e. in a direction opposite to the centre.) Note :(i) Facing the same direction means if one person faces the centre then the other also faces the centre and vice-versa. (ii) Facing the opposite directions means if one person faces the centre then the other faces outside and vice-versa. (iii) Immediate neighbours facing the same direction means if one person faces the centre then the other also faces the centre and vice-versa. (iv) Immediate neighbours facing the opposite directions means if one person faces the centre then the other faces outside and vice-versa. • R sits second to the right of Y. Only two persons sit between R and W. • P sits to the immediate right of W. W faces outside. • Only one person sits between P and Z. Immediate neighbours of P face opposite directions. • Q sits third to the left of Z. Q is not an immediate neighbour of P. • X faces a direction opposite to that of Y. X is an immediate neighbour of neither Y nor P. • Immediate neighbours of S face same direction. P does not face outside. • R and Q face a direction opposite to that of S.Four of the following five are alike in a certain way based on the direction they are facing and so form a group. Which is the one that does not belong to that group?
....

MCQ-> Study the following information carefully and answer the questions given below: Eight friends — J, K, L, M, N, 0, P and Q — are sitting around a circular table but not necessarily in the same order. Some of them are facing the centre and some of them are facing outside. (i.e. in a direction opposite to the centre.) Facing the same direction means if one person faces the centre then the other also faces the centre and vice-versa. Facing the opposite direction means if one person faces the centre then the other faces outside and vice-versa. Immediate neighbours facing the same direction means if one neighbour faces the centre then the other also faces the centre and vice-versa. Immediate neighbours facing the opposite direction means if one neighbour faces the centre then the other faces outside and vice-versa. • Only one person sits between K and 0. Q sits third to the right of 0. • M sits to the immediate right of Q. Q faces outside. • L sits second to the left of P. P is not an immediate neighbour of 0. • L faces a direction opposite to that of 0. Immediate neighbours of L face opposite directions. • J sits third to the left of N. J is not an immediate neighbour of P nor K. • M and J face a direction same as that of N.Four of the following five are alike in a certain way based on the directions they are forming and so form a group. Which is the one that does not belong to that group?
....

MCQ->The simplified value of $$\frac{3\sqrt7}{\sqrt5+\sqrt2}-\frac{5\sqrt5}{\sqrt2+\sqrt7}+\frac{2\sqrt2}{\sqrt7+\sqrt5}$$ is....