Point O is the centre of the circle shown. Line segment AB is 20 units long, line segment CF is 4 units long, and line segment ED is 3 units long. Segments AC, AD, and CD are tangent to the circle at points B, E, and F, respectively. The perimeter of ΔACD isa27 units b50 unitsc51 units d54 units
Question
Point O is the centre of the circle shown. Line segment AB is 20 units long, line segment CF is 4 units long, and line segment ED is 3 units long. Segments AC, AD, and CD are tangent to the circle at points B, E, and F, respectively. The perimeter of ΔACD isa27 units b50 unitsc51 units d54 units
Solution
To solve this problem, we need to understand that in a circle, the lengths of the tangents drawn from an external point to the circle are equal.
Here, the external point is A and the tangents are AB and AD. So, AB = AD = 20 units.
Similarly, the external point is C and the tangents are CF and CD. So, CF = CD = 4 units.
Now, we can find the perimeter of ΔACD by adding the lengths of its sides.
Perimeter of ΔACD = AC + CD + AD
We know that AC = AB = 20 units, CD = CF = 4 units, and AD = AB = 20 units.
So, Perimeter of ΔACD = 20 units + 4 units + 20 units = 44 units.
Therefore, none of the options given are correct. The perimeter of ΔACD is 44 units.
Similar Questions
and AC are tangents to the circle, centre O. AO is a straight line passing through BC at D. If AO 10.8 cm and OC = 4.3 cm find B a). AC, b). AB, D A c). ∠BAO, d). ∠AOB, e). OD, f). BD, g). ZOBD, h). ∠DBA.
Here are the endpoints of the segments AB, CD, and EF.A−6, 4, B1, 2C−7, 6, D−−5, 1E−1, 8, F−3, 1Follow the directions below.(a) Find the length of each segment.Give an exact answer (not a decimal approximation).=AB10.04
ABCD is a cyclic quadrilateral, ABX is a straight line and PQ is a tangent to the circle at A�Angle °CBX 85= , angle °BAQ 55= and angle °CAD 42=
ABCDEis a circle O . The diameter AC is extended to the point F so that CF=16cm. The line BF is the tangent to the circle at B and FDE is a straight line such that FD=18cm andDE=14cm . The radius of the circle is rcm . Calculate(a) the length in cm of FB(b) the value of r .
Given circle EE with diameter start overline, C, D, end overline CD and radius start overline, E, A, end overline EA . start overline, A, B, end overline AB is tangent to EE at AA. If E, A, equals, 8EA=8 and E, B, equals, 17EB=17, solve for A, BAB. Round your answer to the nearest tenth if necessary. If the answer cannot be determined, click "Cannot be determined."
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.