IMO Level 1- Mathematics Olympiad (SOF) Class 4: Questions 449 - 449 of 614

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Question number: 449

» Geometry

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Question

How many circles are there in the given figure?

Polygon poly7Polygon poly7: Polygon [O, P, 3] Polygon poly7Polygon poly7: Polygon [O, P, 3] Polygon poly8Polygon poly8: Polygon [R, O, 3] Polygon poly8Polygon poly8: Polygon [R, O, 3] Polygon poly9Polygon poly9: Polygon [T, R, 3] Polygon poly9Polygon poly9: Polygon [T, R, 3] Triangle poly10Triangle poly10: Polygon P, D_1, OTriangle poly11Triangle poly11: Polygon O, E_1, RTriangle poly12Triangle poly12: Polygon R, F_1, TQuadrilateral poly13Quadrilateral poly13: Polygon H_1, G_1, I_1, J_1Polygon poly1Polygon poly1: Polygon [E, G, 3] Polygon poly1Polygon poly1: Polygon [E, G, 3] Polygon poly2Polygon poly2: Polygon [G, K, 3] Polygon poly2Polygon poly2: Polygon [G, K, 3] Polygon poly3Polygon poly3: Polygon [K, N, 3] Polygon poly3Polygon poly3: Polygon [K, N, 3] Polygon poly4Polygon poly4: Polygon [N, L_1,3] Polygon poly4Polygon poly4: Polygon [N, L_1,3] Polygon poly5Polygon poly5: Polygon [E, Q_1,3] Polygon poly5Polygon poly5: Polygon [E, Q_1,3] Polygon poly6Polygon poly6: Polygon [L_1, R_1,3] Polygon poly6Polygon poly6: Polygon [L_1, R_1,3] Quadrilateral poly14Quadrilateral poly14: Polygon V, W, P_1, T_1Polygon poly15Polygon poly15: Polygon [P, U_1,3] Polygon poly15Polygon poly15: Polygon [P, U_1,3] Triangle poly16Triangle poly16: Polygon P, U_1, W_1Quadrilateral poly17Quadrilateral poly17: Polygon Z_1, A_2, D_2, E_2Circle cCircle c: Circle through O_1 with center N_1Circle c_1Circle c_1: Circle through B with center ACircle r_1Circle r_1: Circle through G_2 with center F_2Circle c_2Circle c_2: Circle through I_2 with center H_2Circle k_2Circle k_2: Circle through K_2 with center J_2Circle q_2Circle q_2: Circle through M_2 with center L_2Circle c_3Circle c_3: Circle through O_2 with center N_2Circle d_3Circle d_3: Circle through Q_2 with center P_2Circle e_3Circle e_3: Circle through S_2 with center R_2Segment f_1Segment f_1: Segment [O, P] of Polygon poly7Segment g_1Segment g_1: Segment [P, Q] of Polygon poly7Segment h_1Segment h_1: Segment [Q, O] of Polygon poly7Segment i_1Segment i_1: Segment [R, O] of Polygon poly8Segment j_1Segment j_1: Segment [O, S] of Polygon poly8Segment k_1Segment k_1: Segment [S, R] of Polygon poly8Segment l_1Segment l_1: Segment [T, R] of Polygon poly9Segment m_1Segment m_1: Segment [R, U] of Polygon poly9Segment n_1Segment n_1: Segment [U, T] of Polygon poly9Segment s_1Segment s_1: Segment [B_1, C_1] Segment s_2Segment s_2: Segment [B_2, C_2] Segment s_3Segment s_3: Segment [B_3, C_3] Segment oSegment o: Segment [P, D_1] of Triangle poly10Segment p_2Segment p_2: Segment [D_1, O] of Triangle poly10Segment d_1Segment d_1: Segment [O, P] of Triangle poly10Segment r_2Segment r_2: Segment [O, E_1] of Triangle poly11Segment o_1Segment o_1: Segment [E_1, R] of Triangle poly11Segment e_1Segment e_1: Segment [R, O] of Triangle poly11Segment t_1Segment t_1: Segment [R, F_1] of Triangle poly12Segment r_3Segment r_3: Segment [F_1, T] of Triangle poly12Segment f_2Segment f_2: Segment [T, R] of Triangle poly12Segment h_2Segment h_2: Segment [H_1, G_1] of Quadrilateral poly13Segment g_2Segment g_2: Segment [G_1, I_1] of Quadrilateral poly13Segment i_2Segment i_2: Segment [I_1, J_1] of Quadrilateral poly13Segment j_2Segment j_2: Segment [J_1, H_1] of Quadrilateral poly13Segment fSegment f: Segment [E, G] of Polygon poly1Segment gSegment g: Segment [G, I] of Polygon poly1Segment hSegment h: Segment [I, E] of Polygon poly1Segment iSegment i: Segment [G, K] of Polygon poly2Segment jSegment j: Segment [K, M] of Polygon poly2Segment kSegment k: Segment [M, G] of Polygon poly2Segment lSegment l: Segment [K, N] of Polygon poly3Segment mSegment m: Segment [N, K_1] of Polygon poly3Segment nSegment n: Segment [K_1, K] of Polygon poly3Segment pSegment p: Segment [N, L_1] of Polygon poly4Segment qSegment q: Segment [L_1, M_1] of Polygon poly4Segment rSegment r: Segment [M_1, N] of Polygon poly4Segment tSegment t: Segment [E, Q_1] of Polygon poly5Segment aSegment a: Segment [Q_1, R_1] of Polygon poly5Segment bSegment b: Segment [R_1, E] of Polygon poly5Segment eSegment e: Segment [L_1, R_1] of Polygon poly6Segment p_1Segment p_1: Segment [R_1, S_1] of Polygon poly6Segment a_1Segment a_1: Segment [S_1, L_1] of Polygon poly6Segment vSegment v: Segment [V, W] of Quadrilateral poly14Segment wSegment w: Segment [W, P_1] of Quadrilateral poly14Segment p_3Segment p_3: Segment [P_1, T_1] of Quadrilateral poly14Segment t_2Segment t_2: Segment [T_1, V] of Quadrilateral poly14Segment sSegment s: Segment [P, U_1] of Polygon poly15Segment dSegment d: Segment [U_1, V_1] of Polygon poly15Segment q_1Segment q_1: Segment [V_1, P] of Polygon poly15Segment w_1Segment w_1: Segment [P, U_1] of Triangle poly16Segment p_4Segment p_4: Segment [U_1, W_1] of Triangle poly16Segment u_1Segment u_1: Segment [W_1, P] of Triangle poly16Segment z_1Segment z_1: Segment [Z_1, A_2] of Quadrilateral poly17Segment a_2Segment a_2: Segment [A_2, D_2] of Quadrilateral poly17Segment d_2Segment d_2: Segment [D_2, E_2] of Quadrilateral poly17Segment e_2Segment e_2: Segment [E_2, Z_1] of Quadrilateral poly17

Image Shows the Many Circles

Choices

Choice (4)Response

a.

7

b.

8

c.

10

d.

9

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