Advertisements
Advertisements
प्रश्न
In the given figure PT is a tangent to the circle. Chord BA produced meets the tangent PT at P.
Given PT = 20 cm and PA = 16 cm.
- Prove ΔPTB ~ ΔPAT
- Find the length of AB.
उत्तर
a. In ΔPTB and ΔPAT,
∠ PTA = ∠PBT ...(Alternate segment theorem)
∠TPA = ∠BPT ...(Common ∠)
∴ ΔPTB ~ ΔPAT ...(AA axiom)
b. PA × PB = PT2
`\implies` 16(16 + AB) = 400
`\implies` 16 + AB = 25
`\implies` AB = 9 cm
APPEARS IN
संबंधित प्रश्न
Two circle touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.
If the sides of a quadrilateral ABCD touch a circle, prove that : AB + CD = BC + AD.
From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that:
∠AOP = ∠BOP
PT is a tangent to the circle at T. If ∠ABC = 70° and ∠ACB = 50°; calculate:
- ∠CBT
- ∠BAT
- ∠APT
In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle AOB = 140° and angle APC = 80°; find the angle BAC.
ABC is a right triangle with angle B = 90°, A circle with BC as diameter meets hypotenuse AC at point D. Prove that: AC × AD = AB2
In the given figure, XY is the diameter of the circle and PQ is a tangent to the circle at Y.
If ∠AXB = 50° and ∠ABX = 70°, find ∠BAY and ∠APY.
In figure , ABC is an isosceles triangle inscribed in a circle with centre O such that AB = AC = 13 cm and BC = 10 cm .Find the radius of the circle.
In the given figure, AB is the diameter. The tangent at C meets AB produced at Q. If ∠CAB = 34°, find:
- ∠CBA
- ∠CQB
The figure shows a circle of radius 9 cm with 0 as the centre. The diameter AB produced meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ:
