Home
Class 10
MATHS
In the given figure, an isosceles triang...

In the given figure, an isosceles triangle `ABC`, with `AB=AC`, circumscribes a circle. Prove that the point of contact `P` bisects the base `BC`.

Text Solution

Verified by Experts

We know that the tangents to a circle from an external point are equal.
`:.AQ=AR`, `BP=BR`, `CP=CQ`.
Now, `AB=ACimpliesAR+BR=AQ+CQ`
`impliesAR+BP=AR+CPimpliesBP=CP`
`implies P` bisects the base `BC`.
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    RS AGGARWAL|Exercise Exercise 8B|15 Videos

  • CIRCLES

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|15 Videos

  • CIRCLES

    RS AGGARWAL|Exercise Test Yourself|20 Videos

  • ARITHMETIC PROGRESSION

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|30 Videos

  • CONSTRUCTIONS

    RS AGGARWAL|Exercise Test Yourself|10 Videos

Similar Questions

Explore conceptually related problems

An isosceles triangle ABC, with AB = AC, circumscribes a circle, touching BC at P, AC at Q and AB at R. Prove that the contact point P bisects BC.

triangleABC is an isosceles triangle in which AB=AC, circumscribed about a circle. Prove that the base is bisccted by the point of contact.

In the given figure, DeltaABC is an isosceles triangle in which AB=AC and AE bisects angleCAD . Prove that AE||BC .

In the given figure,triangle ABC is circumscribing a circle.Find the length of BC if AF=3cm,FB=4cm and AC=9cm

In the given figure, Delta ABC is circumscribing a circle, then find the length of BC.

In isosceles triangle ABC, D is a point on the base BC produced. Prove that AD gt AB .

In Figure,ABC is an isosceles triangle with AB=AC,BD and CE are two medians of the triangle.Prove that BD=CE

In the given figure, triangle ABC is an isosceles triangle right angled at C with AC = 4 cm. Find the length of AB.