Question

6) In A ABC, MLa = 900, XAB) - 7om, (AC) - 24 cm, then (CB)
a) 15
b) 25
c) 17
d) 24​

Answer 1

Answer:

Let ABC be a triangle with 'A' being the right angle. Let 'W' be a circle tangent to AB at A and tangent to BC at some point D. Suppose W intersects with AC again at E and that CE=3, CD=6. What is BD equal to?

The above diagram represents the question!

Since BA and BD are tangents from external point B to the circle, they would be equal in length and let their length be equal to ‘x’ cm as shown.

Angle A is right angled at A and also the point where the circle is tangent to AB, by tangent perpendicularity theorem, AO will be the radius(equal to ‘r’ cm) and also OD and OE as indicated.

Now, triangles ODC and BAC are similar (A-A test) and ratio of corresponding sides will be equal.

$OR \: DC/OD = AC/AB$

$OR \: 6/r = (2r+3)/x …………………(1)$

$Also,$

$DC^2 = CE \: x \: CA (tangent \: secant \: theorem).$

$OR \: 6^2 = 3 x (2r+3)$

$OR (2r+3) = 12 & r = 4.5 ………………..(2)$

$Substituting \: (2) \: in \: (1),$

$OR \: 6/(4.5) = 12/x$

$OR x = 12 x \: 4.5/6 = 9 cm…(Ans)$

Step-by-step explanation:

Hope this helps! :)