Advertisements
Advertisements
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.
उत्तर
From Q, QA and QP are two tangents to the circle with centre O
Therefore, QA = QP ...(i)
Similarly, from Q, QB and QP are two tangents to the circle with centre O'
Therefore, QB = QP ...(ii)
From (i) and (ii)
QA = QB
Therefore, tangents QA and QB are equal.
APPEARS IN
संबंधित प्रश्न
The radius of a circle is 8 cm. calculate the length of a tangent draw to this circle from a point at a distance of 10 cm from its centre.
In the following figure; If AB = AC then prove that BQ = CQ.
In a triangle ABC, the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively. Calculate:
i)`∠`QPR .
In quadrilateral ABCD; angles D = 90°, BC = 38 cm and DC = 25 cm. A circle is inscribed in this quadrilateral which touches AB at point Q such that QB = 27 cm, Find the radius of the circle.
PT is a tangent to the circle at T. If ∠ABC = 70° and ∠ACB = 50°; calculate:
- ∠CBT
- ∠BAT
- ∠APT
In the following figure, PQ is the tangent to the circle at A, DB is the diameter and O is the centre of the circle. If ∠ADB = 30° and ∠CBD = 60°, calculate:
- ∠QAB,
- ∠PAD,
- ∠CDB.
AB is the diameter and AC is a chord of a circle with centre O such that angle BAC = 30°. The tangent to the circle at C intersects AB produced in D. show that BC = BD.
In the adjoining figure, O is the centre of the circle and AB is a tangent to it at point B. ∠BDC = 65°. Find ∠BAO.
In the given figure, AC = AE. Show that:
- CP = EP
- BP = DP
PT is a tangent to the circle at T. If ∠ ABC = 70° and ∠ ACB = 50° ; calculate : ∠ APT
