Advertisements
Advertisements
Question
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.
Solution
OP = 10 cm; radius OT = 8 cm
∵ OT ⊥ PT
In right ΔOTP,
OP2 = OT2 + PT2
102 = 82 + PT2
PT2 = 100 – 64
PT2 = 36
PT = 6
Length of tangent = 6 cm.
APPEARS IN
RELATED QUESTIONS
From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that:
∠AOP = ∠BOP
In a triangle ABC, the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively. Calculate :
- ∠QOR
- ∠QPR;
given that ∠A = 60°.
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.
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.
Tangent at P to the circumcircle of triangle PQR is drawn. If the tangent is parallel to side, QR show that ΔPQR is isosceles.
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, AC = AE. Show that:
- CP = EP
- BP = DP
TA and TB are tangents to a circle with centre O from an external point T. OT intersects the circle at point P. Prove that AP bisects the angle TAB.
In Fig. AP is a tangent to the circle at P, ABC is secant and PD is the bisector of ∠BPC. Prove that ∠BPD = `1/2` (∠ABP - ∠APB).
In the Figure, PT is a tangent to a circle. If m(∠BTA) = 45° and m(∠PTB) = 70°. Find m(∠ABT).
