✓ Board-verified↻ asked 3×
Mathematics · 2022 · 4 marks
CBSE 2022 · Region 4 · Set 1 · Q11
In Fig.-$\displaystyle 2$, if a circle touches the side QR of $\displaystyle \triangle \mathrm{PQR}$ at S and extended sides PQ and PR at M and N, respectively, then
Fig. $\displaystyle 2$ prove that $\displaystyle \mathrm{PM}=\frac{1}{2}(\mathrm{PQ}+\mathrm{QR}+\mathrm{PR})$In Fig. $\displaystyle 3$, a triangle ABC is drawn to circumscribe a circle of radius $\displaystyle 4$ cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths $\displaystyle 6$ cm and $\displaystyle 8$ cm respectively. If the area of $\displaystyle \triangle \mathrm{ABC}$ is $\displaystyle 84 \mathrm{~cm}^{2}$, find the lengths of sides AB and AC . Fig. $\displaystyle 3$
In Fig.-$\displaystyle 2$, if a circle touches the side QR of $\displaystyle \triangle \mathrm{PQR}$ at S and extended sides PQ and PR at M and N, respectively, then
Fig. $\displaystyle 2$ prove that $\displaystyle \mathrm{PM}=\frac{1}{2}(\mathrm{PQ}+\mathrm{QR}+\mathrm{PR})$
In Fig. $\displaystyle 3$, a triangle ABC is drawn to circumscribe a circle of radius $\displaystyle 4$ cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths $\displaystyle 6$ cm and $\displaystyle 8$ cm respectively. If the area of $\displaystyle \triangle \mathrm{ABC}$ is $\displaystyle 84 \mathrm{~cm}^{2}$, find the lengths of sides AB and AC . Fig. $\displaystyle 3$
Marking-scheme solution
Or
\(\displaystyle \Rightarrow A B=13 \mathrm{~cm}, A C=15 \mathrm{~cm}\)
More from Circles
- Assertion: Radius is the smallest distance of a tangent from the centre of the circle. Reason (R): Radius is…2026 · asked 3×
- Assertion: The tangents drawn at the end points of a diameter of a circle, are parallel. Reason (R): Diameter…2024 · asked 3×
- Prove that the parallelogram circumscribing a circle is a rhombus.2024 · asked 3×
- PQ is tangent to a circle with centre O. If ∠ POR=65^°, then m ∠ PTR is2026 · asked 3×
- Which of the following statements is false?2025 · asked 3×
- Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is:2024 · asked 3×
- In the given figure, if PT is a tangent to a circle with centre O and ∠ TPO=35^°, then the measure of ∠ x is:2024 · asked 3×
- In the given figure, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an…2024 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.