Mathematics
In the given figure, AE and BC intersect each other at point D. If ∠CDE = 90°, AB = 5 cm, BD = 4 cm and CD = 9 cm, find AE.
Circles
2 Likes
Answer
In right angle triangle ABD,
⇒ AB2 = BD2 + AD2
⇒ 52 = 42 + AD2
⇒ 25 = 16 + AD2
⇒ AD2 = 25 - 16
⇒ AD2 = 9
⇒ AD =
⇒ AD = 3 cm.
We know that,
If two chords of circle intersect internally or externally then the product of the lengths of their segment is equal.
⇒ AD × DE = CD × BD
⇒ 3 × DE = 9 × 4
⇒ DE =
⇒ DE = 12 cm.
From figure,
AE = AD + DE = 3 + 12 = 15 cm.
Hence, AE = 15 cm.
Answered By
2 Likes
Related Questions
In the figure, given below, AC is a transverse common tangent to two circles with centers P and Q and of radii 6 cm and 3 cm respectively. Given that AB = 8 cm, calculate PQ.
In the given circle with centre O, angle ABC = 100°, ∠ACD = 40° and CT is a tangent to the circle at C. Find ∠ADC and ∠DCT.
In the figure, given below, O is the center of the circumcircle of triangle XYZ. Tangents at X and Y intersect at point T. Given ∠XTY = 80° and ∠XOZ = 140°, calculate the value of ∠ZXY.
In the figure given below, O is the center of the circle and SP is a tangent. If ∠SRT = 65°, find the values of x, y and z.
