The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Solution and Explanation
Let us consider a circle centered at point O.
AB is a tangent drawn on this circle from point A.
Given that,
OA = 5 cm and AB = 4 cm
In ΔABO,
OB ⊥ AB (Radius ⊥ tangent at the point of contact)
Applying Pythagoras theorem in ΔABO, we obtain
AB2 + BO2 = OA2
42 + BO2 = 52
16 + BO2 = 25
BO2 = 25-16
BO2 = 9
BO = 3
Hence, the radius of the circle is 3 cm.
Top Questions on Number of Tangents from a Point on a Circle
- Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
- CBSE Class X
- Mathematics
- Number of Tangents from a Point on a Circle
- In Fig. 10.13, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ∠AOB = 90°.
Fig. 10.13 - CBSE Class X
- Mathematics
- Number of Tangents from a Point on a Circle
- Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
- CBSE Class X
- Mathematics
- Number of Tangents from a Point on a Circle
- Prove that the parallelogram circumscribing a circle is a rhombus.
- CBSE Class X
- Mathematics
- Number of Tangents from a Point on a Circle
- Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
- CBSE Class X
- Mathematics
- Number of Tangents from a Point on a Circle
Questions Asked in CBSE X exam
"जितेंद्र नार्गे जैसे गाइड के साथ किसी भी पर्यटन स्थल का भ्रमण अधिक आनंददायक और यादगार हो सकता है।" इस कथन के समर्थन में 'साना साना हाथ जोड़ि .......' पाठ के आधार पर तर्कसंगत उत्तर दीजिए।
- CBSE Class X - 2025
- प्रश्न उत्तर
आप अदिति / आदित्य हैं। आपकी दादीजी को खेलों में अत्यधिक रुचि है। ओलंपिक खेल-2024 में भारत के प्रदर्शन के बारे में जानकारी देते हुए लगभग 100 शब्दों में पत्र लिखिए।
- CBSE Class X - 2025
- पत्र लेखन
There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to be constructed at a point P on the boundary of the park such that distance of P from A is 35 m more than the distance of P from B. Find distance of point P from A and B respectively.
- CBSE Class X - 2025
- Coordinate Geometry
- Write one function each of the parts - (i) petals (ii) anther (iii) style and (iv) ovary of a bisexual flower.
- CBSE Class X - 2025
- How Do Organisms Reproduce
- In a right triangle ABC, right-angled at A, if $\sin B = \dfrac{1}{4}$, then the value of $\sec B$ is
- CBSE Class X - 2025
- Trigonometry