Question

Question 5 Five diagrams are given below. Figure 1 Figure 2 Figure 3 Figure 4 Figure 5

Answer 1

1. Circles F and G have exactly four common Tangents. Any two circle that do not intensed and have no common regim, Internal Temply intersection) have exactly four common tangerfs. Therefore, the statement is TRUE tangents Extend tangents 2. Circle F and langents. G has exactly two common internof common U Any langent between two circles is is a common internes tangent if the intersection of Me Tangent and the line segment joining the centers of me Two circles is not empty je if the tangen doe intersect with line sogment joining the centers of me two circles." with empły interstiem Any two non-intersecting circle have exachly two common intement Tangent (see figure above), Therefore, the given statement is TRUE.

3. Cirche in figur a an concentric circles, Circles that have a common comer are said to be Concentric circler Sinu, The Two circles in fig. 2. I have the same point c as contor, therefore they are concentric So, the statement on TRUE. 4. Circles F and G are extema - Two circles that do not touch each other Cannot be tangerial to each other, instermally or externally. Since F and G are non-intersecting circles, they are not externally Tangens. So, he given stalement in FALSE. 5. Circles A anol B mu exactly two commm bargentes. Cinte ed and B intersect exactly at one point and their inleznors (excluding perimeters) have emply intense dion e. their intenors have no common region. Such circle an said to be externally Jongens. All externally Tangeant circles have two common external Tangenes and one common internet tangent.

e in total there an three common Targents between externally Tangent circles. Therfor. The given statement is FALSE. 6. Circles A and B an externally Tangent. This statement is True (see exploration for #6) 7 Circles D and E are externally Tangents Circles D and € intersect exactly at one point but the intersection of meir interiors is not emply in fact t is contained with in D. Such circles an said to be inkemetly Tangen. So, the giren statement is FALSE, Note: Internally Tangent circles have excully one common external targent. ③ Circles F and G have exactly four commm external Tanger. Common external Tangents between two circle an Those common Targents which do not intersect with line joining the centers of the circles. . The fore, and G have only two common external Tangents. (See fig. in #0) So, the given slalement is faese.

Since, stalments # 1, 2, 3 and 6 are the only correct slavements, therefore the comit answer is: option C) 1236